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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Families, moduli, classification: algebraic theory, Special surfaces, Rational and ruled surfaces, Elliptic surfaces, elliptic or Calabi-Yau fibrations, \(K3\) surfaces and Enriques surfaces, Surfaces of general type, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to several complex variables and analytic spaces, Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces, Compact complex surfaces, Transcendental methods of algebraic geometry (complex-analytic aspects), Research exposition (monographs, survey articles) pertaining to algebraic geometry, History of algebraic geometry, Collected or selected works; reprintings or translations of classics
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Rational and ruled surfaces, Divisors, linear systems, invertible sheaves, Picard groups, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Effectivity, complexity and computational aspects of algebraic geometry
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Bernardi A.: Ideals of varieties parameterizing certain symmetric tensors. J. P. A. Algebra 212(6), 1542--1559 (2008) Projective techniques in algebraic geometry, Rational and ruled surfaces, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Arithmetic ground fields for curves, Arithmetic ground fields for surfaces or higher-dimensional varieties, Rational and ruled surfaces, Fano varieties, Varieties over global fields
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces G. Popescu, Berezin transforms on noncommutative polydomains, preprint (2013), ; to appear in Trans. Amer. Math. Soc. Canonical models for contractions and nonselfadjoint linear operators, Other ``noncommutative'' mathematics based on \(C^*\)-algebra theory, Several-variable operator theory (spectral, Fredholm, etc.), Noncommutative algebraic geometry
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Finite-dimensional division rings, Quadratic forms over general fields, Forms over real fields, Brauer groups (algebraic aspects), Skew fields, division rings, Algebraic functions and function fields in algebraic geometry, Rational and ruled surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Actions of groups on commutative rings; invariant theory, Rational and ruled surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces N. Prabhu-Naik, Tilting bundles on toric Fano fourfolds, J. Algebra, 471 (2017), 348--398. Noncommutative algebraic geometry, Cluster algebras, Homogeneous spaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Equisingularity (topological and analytic), Noncommutative algebraic geometry, Group actions on varieties or schemes (quotients), Poisson manifolds; Poisson groupoids and algebroids
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Families, moduli, classification: algebraic theory, Fibrations, degenerations in algebraic geometry, Elliptic surfaces, elliptic or Calabi-Yau fibrations, Rational and ruled surfaces, \(K3\) surfaces and Enriques surfaces, Minimal model program (Mori theory, extremal rays)
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Treibich, A. and Verdier, J.-L. , Variétés de Kritchever des Solitons Elliptiques de KP , Preprint. Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, KdV equations (Korteweg-de Vries equations), Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), Soliton equations, Elliptic curves, Rational and ruled surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces \(3\)-folds, Picard groups, Rational and ruled surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Fano varieties, Rational and ruled surfaces, Notions of stability for complex manifolds
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Fibrations, degenerations in algebraic geometry, Families, moduli, classification: algebraic theory, Rational and ruled surfaces, Vector bundles on surfaces and higher-dimensional varieties, and their moduli
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Lowen, W.: Grothendieck categories and their deformations with an application to schemes. Mat. contemp. 41, 27-48 (2012) Noncommutative algebraic geometry, Module categories in associative algebras, Deformations of associative rings
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Global theory and resolution of singularities (algebro-geometric aspects), Rational and ruled surfaces, Singularities in algebraic geometry, Singularities of surfaces or higher-dimensional varieties, Modifications; resolution of singularities (complex-analytic aspects)
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Bogomolov, F.; Prokhorov, Yu., On stable conjugacy of finite subgroups of the plane Cremona group. I, Cent. Eur. J. Math., 11, 12, 2099-2105, (2013) Birational automorphisms, Cremona group and generalizations, Rational and ruled surfaces, Automorphisms of surfaces and higher-dimensional varieties
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Keum, J, Wild \(p\)-cyclic actions on smooth projective surfaces with \(p_g=q=0\), J. Algebra, 244, 45-58, (2001) Automorphisms of surfaces and higher-dimensional varieties, Rational and ruled surfaces, Elliptic surfaces, elliptic or Calabi-Yau fibrations, Global theory and resolution of singularities (algebro-geometric aspects)
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Surfaces of general type, Rational and ruled surfaces, Computational aspects of algebraic surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Sela, Z., ''Diophantine geometry over groups, VIII: Stability,'' Annals of Mathematics (2), vol. 177 (2013), 787--868. Algebraic geometry over groups; equations over groups, Hyperbolic groups and nonpositively curved groups, Free nonabelian groups, Classification theory, stability, and related concepts in model theory, Decidability of theories and sets of sentences, Basic properties of first-order languages and structures, Model-theoretic algebra, Applications of logic to group theory, Noncommutative algebraic geometry, Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Di Gennaro R.: On the structure of the Hartshorne-Rao module of curves on surfaces of minimal degree. Comm. Algebra 33(8), 2749--2763 (2005) Plane and space curves, Rational and ruled surfaces, Divisors, linear systems, invertible sheaves, Linkage
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces I. V. Chirkov and M. A. Shevelin, ''Zero divisors in amalgamated free products of Lie algebras,'' Sib. Math. J., 45, No. 1, 188--195 (2004). Identities, free Lie (super)algebras, Noncommutative algebraic geometry
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Projective techniques in algebraic geometry, Rational and ruled surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces C. McMullen, \(Dynamics on blowups of the projective plane\), Publ. Math. I.H.E.S. 105, 49-89 (2007) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets, Entropy and other invariants, isomorphism, classification in ergodic theory, Rational and ruled surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Embeddings in algebraic geometry, Divisors, linear systems, invertible sheaves, Rational and ruled surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Derived categories of sheaves, dg categories, and related constructions in algebraic geometry, Derived categories and associative algebras, Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc., Quadratic and Koszul algebras, Rings arising from noncommutative algebraic geometry, Derived categories, triangulated categories
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Rationality questions in algebraic geometry, Birational automorphisms, Cremona group and generalizations, Rational and ruled surfaces, Fibrations, degenerations in algebraic geometry, Families, moduli, classification: algebraic theory
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces F. Kirwan, ''Moduli spaces of degree \(d\) hypersurfaces in \({\mathbf P}_n\),'' Duke Math. J., vol. 58, iss. 1, pp. 39-78, 1989. (Co)homology theory in algebraic geometry, Geometric invariant theory, Families, moduli, classification: algebraic theory, Group actions on varieties or schemes (quotients), \(K3\) surfaces and Enriques surfaces, Rational and ruled surfaces, Algebraic moduli problems, moduli of vector bundles
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces D.-Q. Zhang, Automorphisms of finite order on Gorenstein del Pezzo surfaces , Trans. Amer. Math. Soc. 354 (2002), 4831-4845. JSTOR: Automorphisms of surfaces and higher-dimensional varieties, Rational and ruled surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces A. N. Zubkov, \textit{Some homological properties of} GL(\(m\)|\(n\)) \textit{in arbitrary characteristic}, J. Algebra Appl. \textbf{15} (2016), no. 7, 1650119, 26 pp. Supervarieties, Noncommutative algebraic geometry, Group schemes
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Angeleri Hügel, L., Kussin, D.: Large tilting sheaves over weighted noncommutative regular projective curves (2016). Preprint arXiv:1508.03833 Noncommutative algebraic geometry, Special algebraic curves and curves of low genus, Elliptic curves, Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Jaka Cimprič, A method for computing lowest eigenvalues of symmetric polynomial differential operators by semidefinite programming, J. Math. Anal. Appl. 369 (2010), no. 2, 443 -- 452. Semidefinite programming, Nonconvex programming, global optimization, Numerical mathematical programming methods, Noncommutative algebraic geometry
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Cheltsov, I.: Del Pezzo surfaces and local inequalities. In: Automorphisms in Birational and Affine Geometry. Springer Proc. Math. Stat., vol.~\textbf{79}, Springer, Cham, pp.~83-101 (2014) Rational and ruled surfaces, Rational and birational maps, Fano varieties, Computational aspects of algebraic surfaces, Kähler-Einstein manifolds
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Birational automorphisms, Cremona group and generalizations, Symplectic structures in 4 dimensions, Rational and ruled surfaces, Finite transformation groups, Symplectic and contact topology in high or arbitrary dimension, Global theory of symplectic and contact manifolds
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces O. Schiffmann and E. Vasserot, \textit{Cherednik algebras, W algebras and the equivariant cohomology of the moduli space of instantons on A}2, arXiv:1202.2756. Noncommutative algebraic geometry, Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory), String and superstring theories; other extended objects (e.g., branes) in quantum field theory
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Rational and ruled surfaces, Hypersurfaces and algebraic geometry
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces External book reviews, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Research exposition (monographs, survey articles) pertaining to number theory, Schemes and morphisms, Generalizations (algebraic spaces, stacks), Noncommutative algebraic geometry, Finite ground fields in algebraic geometry, Witt vectors and related rings, Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses, Arithmetic varieties and schemes; Arakelov theory; heights, \(K\)-theory of schemes, Collections of articles of miscellaneous specific interest
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Zhang D.-Q.: Normal Algebraic Surfaces with trivial tricanonical divisors. Publ. RIMS. Kyoto Univ. 33, 427--442 (1997) \(K3\) surfaces and Enriques surfaces, Divisors, linear systems, invertible sheaves, Rational and ruled surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Stéphane Chauvin and Cindy De Volder, Some very ample and base point free linear systems on generic rational surfaces, Math. Nachr. 245 (2002), 45 -- 66. , https://doi.org/10.1002/1522-2616(200211)245:13.0.CO;2-L Divisors, linear systems, invertible sheaves, Rational and ruled surfaces, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Vanishing theorems in algebraic geometry
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Surfaces in Euclidean and related spaces, Special algebraic curves and curves of low genus, Complex multiplication and moduli of abelian varieties, Euclidean analytic geometry, Polar geometry, symplectic spaces, orthogonal spaces, Projective analytic geometry, Rational and ruled surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Rational and ruled surfaces, Grassmannians, Schubert varieties, flag manifolds, Eigenvalues, singular values, and eigenvectors, Multilinear algebra, tensor calculus
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Rational and ruled surfaces, Computational aspects of algebraic surfaces, Rational and birational maps, Surfaces of general type, Hypersurfaces and algebraic geometry
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces A. Calabri, On rational and ruled double planes, Ann. Mat. Pura Appl. 181 (2002), 365--387. Rational and ruled surfaces, Birational automorphisms, Cremona group and generalizations
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Petter Andreas Bergh and Dag Madsen, Hochschild homology and split pairs, Bull. Sci. Math. 134 (2010), no. 7, 665 -- 676. (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.), Rings arising from noncommutative algebraic geometry, Complete intersections
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative geometry (à la Connes), Noncommutative algebraic geometry, Methods of noncommutative geometry in general relativity, Representations of quivers and partially ordered sets
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Singularities of surfaces or higher-dimensional varieties, Families, moduli, classification: algebraic theory, Rational and ruled surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative algebraic geometry, Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Yu. Polyakova, Factorization of birational mappings of rational surfaces over the field of real numbers. Fundam. Prikl. Mat. 3(2), 519-547 (1997) Rational and birational maps, Rational and ruled surfaces, Real algebraic and real-analytic geometry
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Rational and ruled surfaces, Formal methods and deformations in algebraic geometry, \(n\)-folds (\(n>4\))
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces U. Derenthal, On a constant arising in Manin's Conjecture for Del Pezzo surfaces. Math. Res. Letters 14 (2007), 481-489. Zbl1131.14042 MR2318651 Rational and ruled surfaces, Rational points, Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.)
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Elliptic surfaces, elliptic or Calabi-Yau fibrations, Rational and ruled surfaces, Arithmetic ground fields for surfaces or higher-dimensional varieties
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Rational and ruled surfaces, Fibrations, degenerations in algebraic geometry, Computational aspects of algebraic surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Harbourne, B.: Rational surfaces with \textit{K}\^{}\{2\}\ >\ 0. Proc. Am. Math. Soc. 124(3), 727-733 (1996) Rational and ruled surfaces, Divisors, linear systems, invertible sheaves, Computational aspects and applications of commutative rings
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Cryptography, Computational aspects of associative rings (general theory), Applications to coding theory and cryptography of arithmetic geometry, Algebraic coding theory; cryptography (number-theoretic aspects), Endomorphism rings; matrix rings
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Vioreanu, B. G.: Mordell-Weil problem for cubic surfaces, numerical evidence, Clay math. Proc. 8, 223-240 (2009) Varieties over global fields, Heights, Rational and ruled surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Colliot-Thélène, J. -L.; Karpenko, N. A.; Merkurjev, A. S.: Rational surfaces and canonical dimension of pgl6, Algebra i analiz 19, No. 5, 159-178 (2007) Group actions on varieties or schemes (quotients), Linear algebraic groups over arbitrary fields, Rational and ruled surfaces, Group schemes
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative algebraic geometry, Plane and space curves, Affine geometry, Group rings, Simple and semisimple modules, primitive rings and ideals in associative algebras, Representations of orders, lattices, algebras over commutative rings
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Lang, William E., Extremal rational elliptic surfaces in characteristic \(p\). I. Beauville surfaces, Math. Z., 0025-5874, 207, 3, 429-437, (1991) Finite ground fields in algebraic geometry, Elliptic surfaces, elliptic or Calabi-Yau fibrations, Rational and ruled surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Y. Yuan, Determinant line bundles on moduli spaces of pure sheaves on rational surfaces and Strange Duality , preprint, [math.AG]. 1005.3201v2 Fine and coarse moduli spaces, Rational and ruled surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative algebraic geometry
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Automorphisms and endomorphisms, Brauer groups of schemes, Vector and tensor algebra, theory of invariants, Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics, Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series, Representations of finite symmetric groups, Combinatorial aspects of representation theory, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.)
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative algebraic geometry, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Quadratic and Koszul algebras, Yang-Baxter equations, Noncommutative algebraic geometry
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces V. Ginzburg, ''Harish-Chandra bimodules for quantized Slodowy slices,'' Represent. Theory, vol. 13, pp. 236-271, 2009. Coadjoint orbits; nilpotent varieties, Noncommutative algebraic geometry, Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Fioresi R. and Gavarini F., On the construction of Chevalley supergroups, Supersymmetry in Mathematics and Physics (Los Angeles 2010), Lecture Notes in Math. 2027, Springer, Berlin (2011), 101-123. Supervarieties, Noncommutative algebraic geometry, Modular Lie (super)algebras, Supermanifolds and graded manifolds
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative algebraic geometry, Variation of Hodge structures (algebro-geometric aspects), \(A_{\infty}\)-categories, relations with homological mirror symmetry, Period matrices, variation of Hodge structure; degenerations
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Vector bundles on surfaces and higher-dimensional varieties, and their moduli, Rational and ruled surfaces, Algebraic moduli problems, moduli of vector bundles, Sheaves in algebraic geometry
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Uematsu, T.: Symbolic generators of the Brauer group of diagonal cubic surfaces and their applications to zero-cycles. RIMS Kokyuroku Bessatsu, Algebraic Number Theory and Related Topics (2012, to appear) Brauer groups of schemes, Symbols and arithmetic (\(K\)-theoretic aspects), Galois cohomology, Rational and ruled surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces M. G. Amaglobeli, ''G-identities of nilpotent groups, I,'' Algebra Logika, 40, No. 1, 3--21 (2001). Quasivarieties and varieties of groups, Noncommutative algebraic geometry, Nilpotent groups, General structure theorems for groups, Geometric group theory, Category of groups
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Geramita, A. V.; Harbourne, B.; Migliore, J., Classifying Hilbert functions of fat point subschemes in \(\mathbb P^2\), Collect. Math., 60, 159-192, (2009) Divisors, linear systems, invertible sheaves, Rational and ruled surfaces, Syzygies, resolutions, complexes and commutative rings, Low codimension problems in algebraic geometry, Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Automorphisms and endomorphisms, Ordinary and skew polynomial rings and semigroup rings, Actions of groups and semigroups; invariant theory (associative rings and algebras), Polynomial rings and ideals; rings of integer-valued polynomials, Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces General topology of 4-manifolds, Low-dimensional topology of special (e.g., branched) coverings, Higher-dimensional knots and links, Rational and ruled surfaces, Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants)
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Derived categories and commutative rings, Noncommutative algebraic geometry
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces R. Bocklandt, \textit{Generating toric noncommutative crepant resolutions}, arXiv:1104.1597 [INSPIRE]. Noncommutative algebraic geometry, Toric varieties, Newton polyhedra, Okounkov bodies, Global theory and resolution of singularities (algebro-geometric aspects)
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces S. Pinansky. Quantum deformations from toric geometry. \textit{Journal of High Energy Physics} (2006), 055, 26~pp. (electronic). String and superstring theories; other extended objects (e.g., branes) in quantum field theory, Toric varieties, Newton polyhedra, Okounkov bodies, Supersymmetric field theories in quantum mechanics, Rational and ruled surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Foundations of algebraic geometry, Associative rings of functions, subdirect products, sheaves of rings
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces F. Oort, ''Endomorphism Algebras of Abelian Varieties,'' in Algebraic Geometry and Commutative Algebra (Kinokuniya, Tokyo, 1988), Vol. 2, pp. 469--502. Algebraic theory of abelian varieties, Complex multiplication and abelian varieties, Endomorphism rings; matrix rings, Arithmetic ground fields for abelian varieties
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces A. Lanteri and F. Tonoli, Ruled surfaces with small class, Comm. Algebra 24 (1996), 3501--3512. Rational and ruled surfaces, Divisors, linear systems, invertible sheaves, \(n\)-folds (\(n>4\))
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces L. Fuentes García, M. Pedreira Pérez, The generic special scroll of genus g in \(\mathbb{P}\)\textit{N}: special scrolls in \(\mathbb{P}\)3. \textit{Commun. Algebra} 40 (2012), 4483-4493. Zbl 1272.14027 Rational and ruled surfaces, Special algebraic curves and curves of low genus, Vector bundles on curves and their moduli
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Schröer, S, Normal del Pezzo surfaces containing a nonrational singularity, Manuscr. Math., 104, 257-274, (2001) Singularities of surfaces or higher-dimensional varieties, Rational and ruled surfaces, Arithmetic ground fields for surfaces or higher-dimensional varieties, Special surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Lahyane, M.: Exceptional curves on smooth rational surfaces with \(-\)\ \textit{K} not nef and of self-intersection zero. Proc. Am. Math. Soc. 133, 1593-1599 (2005) Rational and ruled surfaces, Rational and birational maps, Divisors, linear systems, invertible sheaves
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Applications to coding theory and cryptography of arithmetic geometry, Cryptography, Curves over finite and local fields, Algebraic coding theory; cryptography (number-theoretic aspects), Elliptic curves, Rational and ruled surfaces, Elliptic surfaces, elliptic or Calabi-Yau fibrations, Calabi-Yau manifolds (algebro-geometric aspects), \(3\)-folds, Rational and birational maps, Rationality questions in algebraic geometry, Finite ground fields in algebraic geometry
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces A. Ikeda, 'Stability conditions on CYN categories associated to An-quivers and period maps', \textit{Math. Ann.}367 (2017) 1-49. Calabi-Yau manifolds (algebro-geometric aspects), Noncommutative algebraic geometry, Representations of quivers and partially ordered sets, Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), Representations of associative Artinian rings, Derived categories and associative algebras
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Singularities of surfaces or higher-dimensional varieties, Fano varieties, Rational and ruled surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces I. Cheltsov, J. Park and J. Won, Cylinders in del Pezzo surfaces, preprint (2015), . Divisors, linear systems, invertible sheaves, Rational and birational maps, Singularities of surfaces or higher-dimensional varieties, Rational and ruled surfaces, Fano varieties, Group actions on affine varieties, Affine fibrations
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Formal methods and deformations in algebraic geometry, Differential graded algebras and applications (associative algebraic aspects), Deformation quantization, star products, Polycategories/dioperads, properads, PROPs, cyclic operads, modular operads, Noncommutative algebraic geometry, Quantization in field theory; cohomological methods, Chain complexes (category-theoretic aspects), dg categories
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Fedor Bogomolov and Yuri Tschinkel, Special elliptic fibrations, The Fano Conference, Univ. Torino, Turin, 2004, pp. 223 -- 234. Fibrations, degenerations in algebraic geometry, \(n\)-folds (\(n>4\)), Generalizations (algebraic spaces, stacks), Rational and ruled surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Daniyarova E. Yu., Myasnikov A. G., and Remeslennikov V. N., ''Algebraic geometry over algebraic structures. VI. Geometrical equivalence,'' Algebra and Logic (to be published). Algebraic structures, Equational classes, universal algebra in model theory, Noncommutative algebraic geometry
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Biancofiore A., Livorni E.L.:Algebraic ruled surfaces with low sectional genus.Ricerche di Matematica.Vol.XXXVI,fasc.1{\(\deg\)} (1987) Divisors, linear systems, invertible sheaves, Rational and ruled surfaces, Moduli, classification: analytic theory; relations with modular forms
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Rational and ruled surfaces, Fibrations, degenerations in algebraic geometry
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Polishchuk, A.; Rothstein, M., Fourier transform for \textit{D}-algebras, Duke math. J., 109, 1, 123-146, (2001) Noncommutative algebraic geometry, Algebraic theory of abelian varieties
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Quantum groups and related algebraic methods applied to problems in quantum theory, Quantum groups (quantized enveloping algebras) and related deformations, Lie algebras of linear algebraic groups, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Estimation in multivariate analysis, Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Rational and ruled surfaces, Rational and unirational varieties, Low codimension problems in algebraic geometry
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Eckl, T., Ciliberto--miranda degenerations of \(\mathbb{C} \mathbb{P}^2\) blown up in 10 points, J. Pure Appl. Algebra, 215, 672-696, (2011) Rational and ruled surfaces, Divisors, linear systems, invertible sheaves
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Cryptography, Authentication, digital signatures and secret sharing, Computational aspects of associative rings (general theory), Applications to coding theory and cryptography of arithmetic geometry, Algebraic coding theory; cryptography (number-theoretic aspects), Endomorphism rings; matrix rings
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Brauer groups (algebraic aspects), Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.), Groupoids, semigroupoids, semigroups, groups (viewed as categories), Noncommutative algebraic geometry
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Veys, W.: Vanishing of principal value integrals on surfaces. J. Reine Angew. Math. 598, 139--158 (2006). MR MR2270570 (2007g:11156) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Motivic cohomology; motivic homotopy theory, Rational and ruled surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Elliptic curves, Noncommutative topology, Noncommutative algebraic geometry
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Rings of differential operators (associative algebraic aspects), Automorphisms and endomorphisms, Group actions on varieties or schemes (quotients), Rings arising from noncommutative algebraic geometry
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Bodzenta, A., DG categories and exceptional collections, Proc. Am. Math. Soc., 143, 5, 1909-1923, (2015) Rational and ruled surfaces
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