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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system linear syzygies; graded Betti numbers; partial elimination ideals; inner projection; varieties of small degree Han, K.; Kwak, S.: Sharp bounds for higher linear syzygies and classifications of projective varieties. Math. ann. 361, No. 1, 535-561 (2015) Projective techniques in algebraic geometry, Syzygies, resolutions, complexes and commutative rings, Varieties of low degree, Questions of classical algebraic geometry Sharp bounds for higher linear syzygies and classifications of projective varieties
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system multiplicity; local ring; graded linear series; projective scheme; volume of a line bundle; Kodaira-Iitaka dimension S. D. Cutkosky, ''Multiplicities of graded families of linear series and ideals,'' arXiv: 1301.5613 [math.AG]. Multiplicity theory and related topics, Divisors, linear systems, invertible sheaves, Schemes and morphisms Asymptotic multiplicities of graded families of ideals and linear series
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system neural network of final ring; secret sharing schemes; system of residual classes; elliptic curves Elliptic curves, Finite fields (field-theoretic aspects) Elliptic threshold secret division scheme
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system generating functions; transitive permutation factorizations; symmetric functions; Jucys-Murphy elements; contents of partitions Exact enumeration problems, generating functions, Permutations, words, matrices, Symmetric functions and generalizations, Combinatorial aspects of partitions of integers, Coverings in algebraic geometry Contents of partitions and the combinatorics of permutation factorizations in genus 0
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system purely inseparable extension of exponent 1; Brauer group; p-symbols; transformation formulas; differential p-crossed products Inseparable field extensions, Brauer groups of schemes Remarks on transformation formulas for p-symbols
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system \(ETH\)-cofinite modules; local cohomology; Serre subcategories; system of ideals Local cohomology and commutative rings, Commutative Noetherian rings and modules, Local cohomology and algebraic geometry Lower bounds of certain general local cohomology modules
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system algorithm for subsystems of a root system; simple elliptic singularities; singular del Pezzo surfaces; Coxeter diagram; intersections of two quadrics; deformations of singularities C.\ T.\ C. Wall, Root systems, subsystems and singularities, J. Alg. Geom. 1 (1992), 597-638. Singularities in algebraic geometry, Singularities of surfaces or higher-dimensional varieties, Computational aspects of algebraic surfaces, Deformations of complex singularities; vanishing cycles Root systems, subsystems and singularities
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system deformation spaces of plane curve singularities; equisingular locus; equigeneric locus; equiclassical locus; dimensions of families of plane curves Diaz, S., and Harris, J.: Ideals associated to deformations of singular plane curves. \textit{Trans. Amer. Math. Soc. }309 (1988), no. 2, 433--468. Singularities of curves, local rings, Families, moduli of curves (algebraic), Formal methods and deformations in algebraic geometry, Deformations of singularities, Global theory and resolution of singularities (algebro-geometric aspects) Ideals associated to deformations of singular plane curves
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system Jacobian variety; rational points; linear pencil of projective plane curves; Mordell-Weil lattices; Manin-Shafarevich theorem; height pairing; Lefschetz pencils of hyperplane sections Shioda, T.: Generalization of a theorem of Manin-Shafarevich. Proc. Japan acad. 69A, 10-12 (1993) Families, moduli of curves (algebraic), Jacobians, Prym varieties, Divisors, linear systems, invertible sheaves, Special surfaces Generalization of a theorem of Manin-Shafarevich
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system motives; triangulated categories; cohomology; weight structures; resolution of singularities; alterations Bondarko, M.V., \(\mathbb{Z} [\frac{1}{p}]\)-motivic resolution of singularities, Compos. math., 147, 1434-1446, (2011) Global theory and resolution of singularities (algebro-geometric aspects), Positive characteristic ground fields in algebraic geometry, (Equivariant) Chow groups and rings; motives, Torsion theories, radicals, Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects), Motivic cohomology; motivic homotopy theory, Étale and other Grothendieck topologies and (co)homologies, Grothendieck groups, \(K\)-theory and commutative rings, Algebraic cycles \(\mathbb Z[1/p]\)-motivic resolution of singularities
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system abelian varieties with complex multiplication; periods of first and second kind; Jacobian of the Fermat curves; linear independence of values of the Beta-function; covering radius Wolfart, J., Der überlagerungsradius gewisser algebraischer kurven und die werte der betafunktion an rationalen stellen, Math. Ann., 273, 1-15, (1985) Coverings of curves, fundamental group, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Transcendence (general theory), Complex multiplication and abelian varieties, Rational points, Jacobians, Prym varieties Der Überlagerungsradius gewisser algebraischer Kurven und die Werte der Betafunktion an rationalen Stellen
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system resolution of singularities; hypersurfaces; Maple Gábor Bodnár and Josef Schicho, Automated resolution of singularities for hypersurfaces, J. Symbolic Comput. 30 (2000), no. 4, 401 -- 428. Global theory and resolution of singularities (algebro-geometric aspects), Computational aspects of algebraic surfaces, Singularities of surfaces or higher-dimensional varieties Automated resolution of singularities for hypersurfaces
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system moduli spaces of linear control systems Helmke U (1985) The topology of a moduli space for linear dynamical systems. Comment Math Helvetici 60: 630--655 Canonical structure, Linear systems in control theory, Families, moduli, classification: algebraic theory, Controllability, Minimal systems representations, Algebraic methods The topology of a moduli space for linear dynamical systems
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system blowups; Matlis dual; adjoint ideal; finitely generated supported ideals Global theory and resolution of singularities (algebro-geometric aspects), Regular local rings, Vanishing theorems in algebraic geometry, Divisors, linear systems, invertible sheaves A vanishing theorem for finitely supported ideals in regular local rings
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system normal excellent equicharacteristic local rings; effective Weil divisor; global functions; Cartier divisor; resolution of singularities Divisors, linear systems, invertible sheaves, Regular local rings, Global theory and resolution of singularities (algebro-geometric aspects) A local version of some results of Zariski
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system Zariski's multiplicity conjecture; topological V-equivalent; topologically equisingular; Le number; aligned singularities Eyral C., IMPAN Lecture Notes 3, in: Topics in Equisingularity Theory (2016) Research exposition (monographs, survey articles) pertaining to algebraic geometry, Singularities in algebraic geometry, Deformations of singularities, Global theory and resolution of singularities (algebro-geometric aspects), Equisingularity (topological and analytic), Milnor fibration; relations with knot theory Topics in equisingularity theory
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system resolution of singularities; equisingularity Orlando Villamayor U., On equiresolution and a question of Zariski, Acta Math. 185 (2000), no. 1, 123 -- 159. Equisingularity (topological and analytic), Global theory and resolution of singularities (algebro-geometric aspects), Modifications; resolution of singularities (complex-analytic aspects) On equiresolution and a question of Zariski
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system constructing minimal models; relative anticanonical model; contraction theorem; cone theorem; flip conjecture; termination conjecture; toric varieties Shokurov, V.V.: Numerical geometry of algebraic varieties. Proc. ICM 1986 (to appear) Minimal model program (Mori theory, extremal rays), Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves Numerical geometry of algebraic varieties
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system Néron desingularization; smoothification; Bass-Quillen conjecture; Artin approximation; residual smoothing Ogoma, T., General Néron desingularization based on the idea of Popescu, J. Algebra, 167, 57-84, (1994) Étale and flat extensions; Henselization; Artin approximation, Regular local rings, Global theory and resolution of singularities (algebro-geometric aspects), Excellent rings General Néron desingularization based on the idea of Popescu
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system resolutions of quotient spaces; pluri-toric resolutions; McKay correspondence Global theory and resolution of singularities (algebro-geometric aspects), Toric varieties, Newton polyhedra, Okounkov bodies, Equisingularity (topological and analytic), Homogeneous spaces and generalizations Pluri-toric resolutions of quotient singularities
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system plane curve singularity; weighted homogeneous polynomial; classification theorem; isolated singularity Kang Chunghyuk: Analytic types of plane curve singularities defined by weighted homogeneous polynomials. Trans. AMS 352(9), 3995--4006 (2000) Equisingularity (topological and analytic), Global theory and resolution of singularities (algebro-geometric aspects) Analytic types of plane curve singularities defined by weighted homogeneous polynomials
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system irregularity; divisor; cyclic coverings; resolution of singularity; vanishing of first cohomology Vaquié, Michel, Irrégularité des revêtements cycliques des surfaces projectives non singulières, Amer. J. math., 114, 6, 1187-1199, (1992), MR 1198299 (94d:14015) Coverings in algebraic geometry, Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Vanishing theorems in algebraic geometry Irregularity of cyclic coverings of nonsingular projective surfaces
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system resolution of singularities; toric variety; toric morphism; transversality Tevelev, J.: On a question of B. Teissier. Collect. math. 65, No. 1, 61-66 (2014) Global theory and resolution of singularities (algebro-geometric aspects), Embeddings in algebraic geometry, Toric varieties, Newton polyhedra, Okounkov bodies, Divisors, linear systems, invertible sheaves, Modifications; resolution of singularities (complex-analytic aspects) On a question of B. Teissier
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system existence of relative Bernstein polynomials; equisingularity H. Biosca, Caractérisation de l'existence de polynômes de Bernstein relatifs associés à une famille d'applications analytiques, C. R. Acad. Sci. Paris Sér. I Math. 325 (1997), no. 4, 395-398. Equisingularity (topological and analytic), Deformations of complex singularities; vanishing cycles, Global theory and resolution of singularities (algebro-geometric aspects) Characterization of the existence of relative Bernstein polynomials associated to a family of analytic maps
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system classification of 3-folds of general type; numerically effective canonical divisor; crepant resolution; canonical models; partial resolution; exceptional prime divisor; terminal singularity; quick singularities M. Reid, \textit{Minimal models of canonical} 3\textit{-folds}, in \textit{Algebraic varieties and analytic varieties (Tokyo, 1981)}, \textit{Adv. Stud. Pure Math.}\textbf{1} (1983) 131, North-Holland, Amsterdam, The Netherlands. \(3\)-folds, Global theory and resolution of singularities (algebro-geometric aspects), Minimal model program (Mori theory, extremal rays), Divisors, linear systems, invertible sheaves, Singularities in algebraic geometry Minimal models of canonical 3-folds
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system simultaneous resolution; valuations; monomialization; local uniformization; function field DOI: 10.1006/jabr.1996.7014 Valuations and their generalizations for commutative rings, Arithmetic theory of algebraic function fields, Singularities in algebraic geometry, Global theory and resolution of singularities (algebro-geometric aspects), Algebraic functions and function fields in algebraic geometry, Regular local rings Local weak simultaneous resolution for high rational ranks
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system graded family; volume; multiplicity; asymptotic polynomial Multiplicity theory and related topics, Regular local rings, Singularities in algebraic geometry, Divisors, linear systems, invertible sheaves Growth of multiplicities of graded families of ideals
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system Newton-Okounkov bodies; flags; exceptional curve valuations; non-positive at infinity valuations Divisors, linear systems, invertible sheaves, Global theory and resolution of singularities (algebro-geometric aspects), Valuations and their generalizations for commutative rings, Toric varieties, Newton polyhedra, Okounkov bodies Newton-Okounkov bodies of exceptional curve valuations
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system meromorphic plane curve; intersection multiplicity; equisingularity; Jacobian conjecture Assi, A.: Meromorphic plane curves. Math. Z. 230(1), 16--183 (1999) Equisingularity (topological and analytic), Global theory and resolution of singularities (algebro-geometric aspects) Meromorphic plane curves
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system Singularities in algebraic geometry, Global theory and resolution of singularities (algebro-geometric aspects), Rational and birational maps, Divisors, linear systems, invertible sheaves, Schemes and morphisms A higher-dimensional generalization of Mumford's rational pullback for Weil divisors
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system glueing polynomials; Newton polyhedron; equisingular locus; plane curves; maximal number of cusps; critical points E. Shustin, Gluing of singular and critical points. \textit{Topology}\textbf{37} (1998), 195-217. MR1480886 Zbl 0905.14008 Global theory and resolution of singularities (algebro-geometric aspects), Equisingularity (topological and analytic), Topological properties in algebraic geometry, Singularities in algebraic geometry, Singularities of curves, local rings Gluing of singular and critical points
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system regular local ring; proper transform; multiplicity; valuation ideals; quadratic transform DOI: 10.1080/00927879408825128 Regular local rings, Multiplicity theory and related topics, Global theory and resolution of singularities (algebro-geometric aspects), Singularities in algebraic geometry Improving ideals by means of quadratic transformations
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system blowing-up an \(n\)-dimensional linear system; resolution; meromorphic foliation; formal power series ring Global theory and resolution of singularities (algebro-geometric aspects), Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\), Formal power series rings, Divisors, linear systems, invertible sheaves Linear systems of power series, pencils and associated foliations
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system negative divisors; rigid divisors; divisors on surfaces; spherelike sheaves Divisors, linear systems, invertible sheaves, Global theory and resolution of singularities (algebro-geometric aspects), Structure of families (Picard-Lefschetz, monodromy, etc.) Rigid divisors on surfaces
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system analytic local ring; resolution of singularities Cutkosky S.D., Duke Math. J 57 pp 175-- (1988) Divisors, linear systems, invertible sheaves, Global theory and resolution of singularities (algebro-geometric aspects), Local rings and semilocal rings Weil divisors and symbolic algebras
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system valuations; regular local rings; resolution of singularities Valuations and their generalizations for commutative rings, Regular local rings, Global theory and resolution of singularities (algebro-geometric aspects) Local uniformization of Abhyankar valuations
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system plane curve singularities; equisingularity; proper transform; exceptional curves; resolution of singular points; blow-up; topological equivalence; analytic equivalence Chunghyuk Kang, Topological classification of irreducible plane curve singularities in terms of Weierstrass polynomials, Proc. Amer. Math. Soc. 123 (1995), no. 5, 1363 -- 1371. Equisingularity (topological and analytic), Complex surface and hypersurface singularities, Global theory of complex singularities; cohomological properties, Global theory and resolution of singularities (algebro-geometric aspects), Singularities of curves, local rings Topological classification of irreducible plane curve singularities in terms of Weierstrass polynomials
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system intersection theory; linear systems; infinitely near base; complete ideals Lejeune-Jalabert, M.: Linear systems with infinitely near base conditions and complete ideals in dimension two. (1991) Divisors, linear systems, invertible sheaves, Regular local rings, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry Linear systems with infinitely near base conditions and complete ideals in dimension two
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system equisingularity; discriminant curve; minimal resolution R. Bondil, Discriminant of a generic projection of a minimal normal surface singularity, C.R. Acad. Sci. Paris, Ser. I 337, 195--200, (2003). Singularities of surfaces or higher-dimensional varieties, Divisors, linear systems, invertible sheaves, Global theory and resolution of singularities (algebro-geometric aspects), Modifications; resolution of singularities (complex-analytic aspects) Discriminant of a generic projection of a minimal normal surface singularity
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system openness of loci; resolution of singularities; excellent rings; resolution of noetherian integral domain; catenary ring; local noetherian rings; lifting Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.), Commutative Noetherian rings and modules, Global theory and resolution of singularities (algebro-geometric aspects), Regular local rings, Rational and birational maps, Dimension theory, depth, related commutative rings (catenary, etc.) Sur le lieu \(U_ R(A)\) d'un anneau noethérien
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system polynomial map; pencil; atypical value; irregular value at infinity; equisingularity; Milnor fibration; Euler numbers; characteristic polynomial; minimal resolution Milnor fibration; relations with knot theory, Global theory and resolution of singularities (algebro-geometric aspects), Equisingularity (topological and analytic) Fibrations associated with a pencil of plane curves
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system resolution of singularities; simple normal crossings; semisimple normal crossings; desingularization invariant; Hilbert-Samuel function; singularities of pairs; log-resolution of singularities Bierstone, Edward; Vera Pacheco, Franklin, Resolution of singularities of pairs preserving semi-simple normal crossings, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matematicas. RACSAM, 107, 159-188, (2013) Global theory and resolution of singularities (algebro-geometric aspects), Modifications; resolution of singularities (complex-analytic aspects), Divisors, linear systems, invertible sheaves, Invariants of analytic local rings Resolution of singularities of pairs preserving semi-simple normal crossings
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system simultaneous resolution; non-log-canonical singularity; equisingular deformation Deformations of singularities, Global theory and resolution of singularities (algebro-geometric aspects), Modifications; resolution of singularities (complex-analytic aspects), Equisingularity (topological and analytic), Global theory of complex singularities; cohomological properties, Deformations of complex singularities; vanishing cycles On \((-P\cdot P)\)-constant deformations of Gorenstein surface singularities
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system smooth morphisms; regular morphisms; smoothing ring morphisms Étale and flat extensions; Henselization; Artin approximation, Local structure of morphisms in algebraic geometry: étale, flat, etc., Regular local rings, Henselian rings, Software, source code, etc. for problems pertaining to commutative algebra, Global theory and resolution of singularities (algebro-geometric aspects) Constructive general Néron desingularization for one dimensional local rings
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system resolution of singularities; stable simple normal crosssings; desingularization invariant; Hilbert-Samuel function; presentations Global theory and resolution of singularities (algebro-geometric aspects), Singularities of surfaces or higher-dimensional varieties, Divisors, linear systems, invertible sheaves, Invariants of analytic local rings, Modifications; resolution of singularities (complex-analytic aspects) Desingularization preserving stable simple normal crossings
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system linear series; asymptotic multiplicity; Zariski decomposition Lesieutre, J.: A pathology of asymptotic multiplicity in the relative setting. (2015) Divisors, linear systems, invertible sheaves, Global theory and resolution of singularities (algebro-geometric aspects) A pathology of asymptotic multiplicity in the relative setting
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system kroneckerian dimension of fields; quadratic transformations; towers; pillars; dicritical divisors Abhyankar, S.S.: Pillars and towers of quadratic transformations. Proc. Am. Math. Soc. 139, 3067--3082 (2011) Relevant commutative algebra, Regular local rings, Valuation rings, Divisors, linear systems, invertible sheaves Pillars and towers of quadratic transformations
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system topological triviality; isolated singularities; deformations of singularities; weighted homogeneous Equisingularity (topological and analytic), Global theory and resolution of singularities (algebro-geometric aspects) Equisingularity for flat deformations and topological rigidity
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system blowing-ups; threefold; canonical singularities; minimal models for on- parameter-families of surfaces Y. Kawamata, Crepant blowing-ups of \(3\)-dimensional canonical singularities and its application to degenerations of surfaces , Tokyo University, preprint. JSTOR: Global theory and resolution of singularities (algebro-geometric aspects), Minimal model program (Mori theory, extremal rays), \(3\)-folds, Divisors, linear systems, invertible sheaves, Singularities in algebraic geometry, Families, moduli, classification: algebraic theory On the crepant blowing-ups of canonical singularities and its application to degenerations of surfaces
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system plane curve singularities; topologically equivalent; analytically equivalent Equisingularity (topological and analytic), Global theory and resolution of singularities (algebro-geometric aspects) Some analytic irreducible plane curve singularities
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system polynomial periodicity for Betti numbers; branched covering; Betti number of a desingularization [Ha2] E. Hironaka,Polynomial periodicity for Betti numbers of covering surfaces, Inventiones Mathematicae108 (1992), 289--321. Coverings in algebraic geometry, Classical real and complex (co)homology in algebraic geometry, Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves Polynomial periodicity for Betti numbers of covering surfaces
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system variety of general type; deformation of singularities; complete intersection; hypersurfaces; geometric genus DOI: 10.1090/S0002-9947-96-01613-3 Complete intersections, Global theory and resolution of singularities (algebro-geometric aspects), Hypersurfaces and algebraic geometry, Divisors, linear systems, invertible sheaves Divisors of generic complete intersections in projective space
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system characteristic divisor on a complex manifold; \(\bmod 2\)-index of the characteristic divisor; desingularizations of isolated Gorenstein singularities Esnault, Hélène; Seade, José; Viehweg, Eckart, Characteristic divisors on complex manifolds, J. Reine Angew. Math., 424, 17-30, (1992) Divisors, linear systems, invertible sheaves, Global theory and resolution of singularities (algebro-geometric aspects), Complex manifolds, Modifications; resolution of singularities (complex-analytic aspects) Characteristic divisors on complex manifolds
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system flow-box theorem; vector field; foliations; resolution of singularities Foliations generated by dynamical systems, Singularities in algebraic geometry, Global theory and resolution of singularities (algebro-geometric aspects), Obstructions to group actions (\(K\)-theoretic aspects), General theory of group and pseudogroup actions, Foliations in differential topology; geometric theory, Equisingularity (topological and analytic), Singularities of holomorphic vector fields and foliations Generalized flow-box property for singular foliations
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system Zariski-Lipman Conjecture; module of derivations; normal algebraic surfaces; non-complete algebraic surfaces Singularities of surfaces or higher-dimensional varieties, Global theory and resolution of singularities (algebro-geometric aspects), Singularities in algebraic geometry, Regular local rings, Derivations and commutative rings On the Zariski-Lipman conjecture for normal algebraic surfaces
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system quotient singularity; resolution of singularities; crepant resolution; Cox ring Global theory and resolution of singularities (algebro-geometric aspects), Minimal model program (Mori theory, extremal rays), McKay correspondence, Group actions on varieties or schemes (quotients), Geometric invariant theory, Divisors, linear systems, invertible sheaves Crepant resolutions of 3-dimensional quotient singularities via Cox rings
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system resolution of singularities; functorial; canonical; marked ideal E. Bierstone, P. Milman, and M. Temkin, \( \mathbb{Q}\)-universal desingularization, arXiv preprint 0905.3580v1 (2009). Global theory and resolution of singularities (algebro-geometric aspects), Modifications; resolution of singularities (complex-analytic aspects), Equisingularity (topological and analytic), Global theory of complex singularities; cohomological properties \(Q\)-universal desingularization
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system smooth morphisms; regular morphisms; Néron desingularization Pfister, G.; Popescu, D., \textit{Construction of Neron Desingularization for Two Dimensional Rings}. arXiv:AC/1612.01827 Étale and flat extensions; Henselization; Artin approximation, Local structure of morphisms in algebraic geometry: étale, flat, etc., Regular local rings, Global theory and resolution of singularities (algebro-geometric aspects) Construction of Néron desingularization for two dimensional rings
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system linear systems; triple points; ruled surfaces Segre, C.: Mehrdimensionale Räume. Encyklopädie der Mathematischen Wissenschaften, vol. 3-2-2a. B.G. Teubner, Leipzig (1912) Families, moduli of curves (algebraic), Families, moduli, classification: algebraic theory, Divisors, linear systems, invertible sheaves, Equisingularity (topological and analytic) Triple-point defective surfaces
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system equisingular deformation; plane curve singularities; Milnor number; Hamburger-Noether expansion; deformation of parameterization Campillo A., Greuel G.-M., Lossen C.: Equisingular deformations of plane curves in arbitrary characteristic. Compos. Math. 143, 829--882 (2007) Deformations of singularities, Local deformation theory, Artin approximation, etc., Global theory and resolution of singularities (algebro-geometric aspects), Singularities of curves, local rings, Equisingularity (topological and analytic) Equisingular deformations of plane curves in arbitrary characteristic
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system geometric monodromy; global monodromy; bifurcation set; critical value at infinity; Lojasiewicz number; Milnor number; Milnor fibration; global monodromy fibration; \(M\)-tame polynomial; primitive polynomial [12]H. V. Hà and T. S. Pha.m, Invariance of the global monodromies in families of polynomials of two complex variables, Acta Math. Vietnam. 22 (1997), 515--526. Milnor fibration; relations with knot theory, Equisingularity (topological and analytic), Critical points and critical submanifolds in differential topology, Global theory and resolution of singularities (algebro-geometric aspects) Invariance of the global monodromies in families of polynomials of two complex variables
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system symbolic powers; weighted projective spaces Cutkosky, SD; Kurano, K., Asymptotic regularity of powers of ideals of points in a weighted projective plane, Kyoto J. Math., 51, 25-45, (2011) Divisors, linear systems, invertible sheaves, General commutative ring theory, Computational aspects of algebraic surfaces, Global theory and resolution of singularities (algebro-geometric aspects) Asymptotic regularity of powers of ideals of points in a weighted projective plane
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system biographies; Oscar Zariski; algebraic geometry; schools of mathematics; algebraic surfaces; singularity theory; linear systems C. Parikh, The unreal life of Oskar Zariski, Springer, 2009. History of algebraic geometry, Biographies, obituaries, personalia, bibliographies, History of mathematics in the 20th century, Schools of mathematics, Surfaces and higher-dimensional varieties, Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves The unreal life of Oscar Zariski
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system Weil divisor; invariants of singularities; base point freeness; adjoint bundles; normal surfaces Kawachi, T.: On the base point freeness of adjoint bundles on normal surfaces. Manuscripta math. 101, 23-38 (2000) Adjunction problems, Singularities of surfaces or higher-dimensional varieties, Divisors, linear systems, invertible sheaves, Global theory and resolution of singularities (algebro-geometric aspects) On the base point freeness of adjoint bundles on normal surfaces
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system equianalytic singularity; flat families of embedded reduced curves; number of singular points; Hilbert scheme; singularities of given analytic type Greuel G.-M., Lossen C.,Equianalytic and equisingular families of curves on surfaces, Manuscripta Math.,91 (1996), 323--342. Singularities of surfaces or higher-dimensional varieties, Global theory and resolution of singularities (algebro-geometric aspects), Singularities of curves, local rings, Equisingularity (topological and analytic) Equianalytic and equisingular families of curves on surfaces
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system affine cone; \(\alpha\)-invariant; anticanonical divisor; cylinder; del Pezzo surface; \(\mathbb{G}_a\)-action; log canonical singularity Cheltsov, I.; Park, J.; Won, J., \textit{affine cones over smooth cubic surfaces}, J. Eur. Math. Soc. (JEMS) Global theory and resolution of singularities (algebro-geometric aspects), Fano varieties, Group actions on affine varieties, Affine fibrations, Divisors, linear systems, invertible sheaves, Rational and birational maps, Singularities of surfaces or higher-dimensional varieties Affine cones over smooth cubic surfaces
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system Equisingularity (topological and analytic), Global theory and resolution of singularities (algebro-geometric aspects) A discriminant criterion for an equivalence of an analytic family of plane curve singularities and its applications
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system blowing-down; effective divisor; contraction; singularities Rational and birational maps, Projective techniques in algebraic geometry, Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Singularities in algebraic geometry Projective contractions along weighted projective spaces
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system non-positive at infinity valuations; plane valuations; singularities Divisors, linear systems, invertible sheaves, Global theory and resolution of singularities (algebro-geometric aspects), Valuations and their generalizations for commutative rings Discrete equivalence of non-positive at infinity plane valuations
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system extremal rays; toric varieties; resolution of a normal surface; minimal model Reid, M., Decomposition of toric morphisms, (Arithmetic and geometry, vol. II, Prog. math., vol. 36, (1983), Birkhäuser Boston Boston, MA), 395-418 \(3\)-folds, Divisors, linear systems, invertible sheaves, Global theory and resolution of singularities (algebro-geometric aspects), Minimal model program (Mori theory, extremal rays), Rational and birational maps Decomposition of toric morphisms
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system algebraic geometry; singularities of algebraic varieties; deformations of singularities; simultaneous embedded resolutions; Milnor number; Newton number; m-jet spaces. Singularities in algebraic geometry, Deformations of singularities, Local structure of morphisms in algebraic geometry: étale, flat, etc., Global theory and resolution of singularities (algebro-geometric aspects), Embeddings in algebraic geometry, Equisingularity (topological and analytic), Local complex singularities, Invariants of analytic local rings Newton non-degenerate \(\mu\)-constant deformations admit simultaneous embedded resolutions
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system canonical hyperplane sections; classification of surfaces; only one effective anticanonical divisor on minimal resolution of singularities; elliptic ruled surfaces Epema, D.: Surfaces with canonical hyperplane sections, Thèse Leiden, cf. aussi: Indagationes Math.45, 173-184 (1983) Families, moduli, classification: algebraic theory, Divisors, linear systems, invertible sheaves, Global theory and resolution of singularities (algebro-geometric aspects), Special surfaces, Singularities of surfaces or higher-dimensional varieties Surfaces with canonical hyperplane sections
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system divisor class group of affine surface P. Blass and J. Lang , A method for computing the kernel of a map of divisor classes of local rings in characteristic p \neq 0 , Mich. Math. J. 35 (1988). Regular local rings, Divisors, linear systems, invertible sheaves, Special surfaces A method for computing the kernel of a map of divisor classes of local rings in characteristic p\(\neq 0\)
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system constructing minimal models; relative anticanonical model; contraction theorem; cone theorem; flip conjecture; termination conjecture; toric varieties Minimal model program (Mori theory, extremal rays), Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves Remarks on the structure of the space of regular algebraic homogeneous mappings
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system analytic germ; topological type; normal singularity; Milnor fibration Pichon, A, Three-dimensional manifolds which are the boundary of a normal singularity \(z^k-f(x, y)\), Mathematische Zeitschrift, 231, 625-654, (1999) Equisingularity (topological and analytic), Milnor fibration; relations with knot theory, Global theory and resolution of singularities (algebro-geometric aspects) Three-dimensional manifolds which are the boundary of a normal singularity \(z^k- f(x,y)\)
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system exceptional divisors; Euler characteristic; embedded resolution of zero set; local zeta function; topological zeta function Global theory and resolution of singularities (algebro-geometric aspects), Topological properties in algebraic geometry, Zeta functions and \(L\)-functions, Divisors, linear systems, invertible sheaves On Euler characteristics associated to exceptional divisors
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system homogeneous ideals; determinantal variety; 0-dimensional subschemes; smooth quadric; ideal sheaf; mapping cone S. Giuffrida, R. Maggioni, and A. Ragusa, Resolutions of 0-dimensional subschemes of a smooth quadric,Zero-dimensional schemes (Ravello, 1992), 191--204, de Gruyter, Berlin, 1994. Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Global theory and resolution of singularities (algebro-geometric aspects), Syzygies, resolutions, complexes and commutative rings, Divisors, linear systems, invertible sheaves Resolutions of \(0\)-dimensional subschemes of a smooth quadric
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system toric variety; fan; toric ideal; blow-up; desingularization; rational singularity; resolution of singularities; divisors David A. Cox, Toric varieties and toric resolutions, Resolution of singularities (Obergurgl, 1997) Progr. Math., vol. 181, Birkhäuser, Basel, 2000, pp. 259 -- 284. Toric varieties, Newton polyhedra, Okounkov bodies, Global theory and resolution of singularities (algebro-geometric aspects), Grassmannians, Schubert varieties, flag manifolds, Divisors, linear systems, invertible sheaves Toric varieties and toric resolutions
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system Rational and birational maps, Divisors, linear systems, invertible sheaves, Global theory and resolution of singularities (algebro-geometric aspects), Positive characteristic ground fields in algebraic geometry, Rational and ruled surfaces Unbounded negativity on rational surfaces in positive characteristic
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system special pencil; dicritical divisors; reduction of an ideal Abhyankar, S.S.: More about dicriticals. Proc. Am. Math. Soc. 139, 3083--3097 (2011) Relevant commutative algebra, Regular local rings, Valuation rings, Divisors, linear systems, invertible sheaves More about dicriticals
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system quotient singularity; symplectic resolution; Cox ring; symplectic manifold Donten-Bury, M.; Wiśniewski, J. A.: On 81 symplectic resolutions of a 4-dimensional quotient by a group of order 32. (2014) Global theory and resolution of singularities (algebro-geometric aspects), Minimal model program (Mori theory, extremal rays), Group actions on varieties or schemes (quotients), Geometric invariant theory, Divisors, linear systems, invertible sheaves, Hyper-Kähler and quaternionic Kähler geometry, ``special'' geometry On 81 symplectic resolutions of a 4-dimensional quotient by a group of order 32
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system unfoldings; deformations; analytic triviality; moduli; equisingularity; versal discriminant; versality discriminant; instability locus; contact equivalence; liftable vector fields; blowing up; blowing down Equisingularity (topological and analytic), Complex surface and hypersurface singularities, Critical points and critical submanifolds in differential topology, Global theory and resolution of singularities (algebro-geometric aspects), Singularities in algebraic geometry On blowing up versal discriminants
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system germ of a normal complex analytic surface singularity; canonical divisor; numerical Gorenstein singularities F. M. Ganter, Properties of - P \cdot P for Gorenstein surface singularities , Math. Z. 223 (1996), 411-419. Divisors, linear systems, invertible sheaves, Singularities of surfaces or higher-dimensional varieties, Global theory and resolution of singularities (algebro-geometric aspects), Germs of analytic sets, local parametrization, Modifications; resolution of singularities (complex-analytic aspects) Properties of \(-P \cdot P\) for Gorenstein surface singularities
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system blowing-up; blow-analytic function; blow-analytic equivalence Equisingularity (topological and analytic), Global theory and resolution of singularities (algebro-geometric aspects), Singularities of curves, local rings, Local complex singularities, Modifications; resolution of singularities (complex-analytic aspects), Singularities in algebraic geometry An elementary exposé on equisingularities
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system Mori theory; desingularisation; log-del Pezzo surface; index; Picard number; multiplicity; non-minimal K3 surfaces; reflection group; Fano manifolds; log-terminal singularities; nef anticanonical class Nikulin, V. V.: Del Pezzo surfaces with log-terminal singularities. III, Math. USSR izv. 35, 657-675 (1990) Singularities of surfaces or higher-dimensional varieties, Divisors, linear systems, invertible sheaves, Picard groups, Special surfaces, Reflection groups, reflection geometries, Global theory and resolution of singularities (algebro-geometric aspects) Del Pezzo surfaces with log-terminal singularities. III
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system rational surface singularity; non-singular point; Cohen-Macaulay point; module of differentials; vanishing of cohomology Local cohomology and algebraic geometry, Homological functors on modules of commutative rings (Tor, Ext, etc.), Regular local rings, Modules of differentials, Singularities in algebraic geometry, Global theory and resolution of singularities (algebro-geometric aspects), Singularities of surfaces or higher-dimensional varieties, Special surfaces Cohomological characterizations of smoothness and the case of rational surface singularities
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system numerically effective canonical divisor; algebraic 3-fold of general type; canonical singularities; canonical ring; desingularization Kawamata, Y, On the finiteness of generators of a pluricanonical ring for a \(3\)-fold of general type, Am. J. Math., 106, 1503-1512, (1984) \(3\)-folds, Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Singularities in algebraic geometry On the finiteness of generators of a pluricanonical ring for a 3-fold of general type
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system quasihomogeneous singularities; classification of singularities Equisingularity (topological and analytic), Global theory and resolution of singularities (algebro-geometric aspects) Analytic types of the surface singularities defined by some weighted homogeneous polynomials
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system non-positive at infinity valuations; rational surfaces; cone of curves Divisors, linear systems, invertible sheaves, Global theory and resolution of singularities (algebro-geometric aspects), Valuations and their generalizations for commutative rings Non-positive and negative at infinity divisorial valuations of Hirzebruch surfaces
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system multiplier ideal; monomial ideal; resolution; local algebra M. Blickle and R. Lazarsfeld, An informal introduction to multiplier ideals, \textit{Trends in commutative algebra, Math. Sci. Res. Inst. Publ.}, \textbf{51}, Cambridge Univ. Press, pp.87-114. Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves An informal introduction to multiplier ideals
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system log category; discrepancy; log canonical threshold; rationality of canonical singularities J. Kollár, Singularities of pairs, Algebraic geometry (Santa Cruz, 1995), Proc. Sympos. Pure Math. 62, American Mathematical Society, 1997, p. 221-287 Singularities in algebraic geometry, Divisors, linear systems, invertible sheaves, Global theory and resolution of singularities (algebro-geometric aspects), \(n\)-folds (\(n>4\)), Singularities of surfaces or higher-dimensional varieties Singularities of pairs
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system González-Sprinberg-Verdier formula; Euler obstruction Sebastiani ( M. ) .- Sur la formule de Gonzalez-Verdier , Bull. Braz. Math. Soc. 16 ( 1985 ), no. 1, p. 31 - 44 . MR 819804 | Zbl 0628.14008 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Singularities in algebraic geometry, Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Obstruction theory in algebraic topology Sur la formule de Gonzalez-Verdier. (On the Gonzalez-Verdier formula)
0
resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system real algebraic variety; semi-algebraic set; polynomial function; normal variety; divisor; bounded polynomial function Plaumann, D.; Scheiderer, C., The ring of bounded polynomials on a semi-algebraic set, Trans. Am. Math. Soc., 364, 4663-4682, (2012) Real algebraic and real-analytic geometry, Divisors, linear systems, invertible sheaves, Global theory and resolution of singularities (algebro-geometric aspects), Real algebraic sets The ring of bounded polynomials on a semi-algebraic set
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system complete ideals; infinitely near points; sandwiches; regular local rings; Cartier divisors Campillo, A., Gonzalez-Sprinberg, G.: On characteristic cones, clusters and chains of infinitely near points. In: Brieskorn Anniversary Volume. Volume 162 of Progress in Mathematics, pp. 251-261. Birkhäuser, Basel (1996) Complete rings, completion, Infinitesimal methods in algebraic geometry, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Divisors, linear systems, invertible sheaves, Regular local rings, Rational and birational maps On characteristic cones, clusters and chains of infinitely near points
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system plane curve; Milnor fibration; mixed Hodge structure; Hodge filtration; Plücker formula; bifurcation set; Betti number; Euler number; critical values at infinity Mixed Hodge theory of singular varieties (complex-analytic aspects), Equisingularity (topological and analytic), Global theory and resolution of singularities (algebro-geometric aspects), Plane and space curves, Milnor fibration; relations with knot theory An affine algebraic type of the Plücker-Milnor formula on \(\mathbb{C}^2\)
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system superficial elements; normal surface singularity; minimality of the Milnor number Bondil ( R. ) , Lê ( D.T. ). - Caractérisations des éléments superficiels d'un idéal , C.R. Acad. Sci. Paris , t. 332 , Sér. I , p. 717 - 722 ( 2001 ). MR 1843194 | Zbl 1006.14013 Singularities of surfaces or higher-dimensional varieties, Regular local rings, Singularities in algebraic geometry, Global theory and resolution of singularities (algebro-geometric aspects) Characterizations of superficial elements of an ideal
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system complex spaces and germs; isolated hypersurface singularities; equisingular deformations; \(\mu\)-constant stratum; embedded deformations; plane curve singularities; parametrization; resolution; normalization; versal deformations; obstructions; cotangent complex G.-M. Greuel, C. Lossen, E. Shustin, \(Introduction to Singularities and Deformations\) (Springer, Berlin, 2007) Deformations of complex singularities; vanishing cycles, Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces, Invariants of analytic local rings, Equisingularity (topological and analytic), Complex surface and hypersurface singularities, Modifications; resolution of singularities (complex-analytic aspects), Deformations of singularities, Singularities of surfaces or higher-dimensional varieties, Global theory and resolution of singularities (algebro-geometric aspects), Research exposition (monographs, survey articles) pertaining to algebraic geometry Introduction to singularities and deformations
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system resolution; exceptional divisor Ishii, S., \textit{extremal functions and prime blow-ups}, Comm. Algebra, 32, 819-827, (2004) Rational and birational maps, Global theory and resolution of singularities (algebro-geometric aspects), Valuations and their generalizations for commutative rings, Singularities in algebraic geometry, Divisors, linear systems, invertible sheaves Extremal functions and prime blow-ups
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system normal surface singularity; resolution of the singularity; canonical divisor; deformation of a normal Gorenstein surface singularity Singularities of surfaces or higher-dimensional varieties, Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves On \(-P\cdot P\) of surface singularities
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Global theory and resolution of singularities (algebro-geometric aspects), Divisors, linear systems, invertible sheaves, Regular local rings, Equisingularity (topological and analytic) Plücker formula and the equisingularity set of a linear system degeneracy locus; desingularization; singular varieties; Chern-Schwartz-MacPherson classes; Euler characteristic; Brill-Noether locus Parusiński, Adam; Pragacz, Piotr, Chern-Schwartz-macpherson classes and the Euler characteristic of degeneracy loci and special divisors, J. amer. math. soc., 8, 4, 793-817, (1995) Divisors, linear systems, invertible sheaves, Topological properties in algebraic geometry, Global theory and resolution of singularities (algebro-geometric aspects), Characteristic classes and numbers in differential topology Chern-Schwartz-MacPherson classes and the Euler characteristic of degeneracy loci and special divisors
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