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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, Configurations and arrangements of linear subspaces, Ideals and multiplicative ideal theory in commutative rings, Polynomial rings and ideals; rings of integer-valued polynomials
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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.: Structure of rational open surfaces with non-positive Euler characteristic. Math. ann. 312, 527-548 (1998) Rational and ruled surfaces, Birational automorphisms, Cremona group and generalizations, Topological properties in algebraic geometry, Families, moduli, classification: algebraic theory, 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 Bauer, Th.; Schmitz, D., Volumes of Zariski chambers, J. Pure Appl. Algebra, 217, 1, 153-164, (2013) 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 \(K3\) surfaces and Enriques surfaces, Automorphisms of surfaces and higher-dimensional varieties, Singularities of surfaces or higher-dimensional varieties, Rational and ruled surfaces, Fano varieties, Research exposition (monographs, survey articles) 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 Divisors, linear systems, invertible sheaves, 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 Group rings, Ordinary and skew polynomial rings and semigroup rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Families, moduli of curves (algebraic)
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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 Gerstenhaber, M., Schack, S.D.: Algebraic cohomology and deformation theory. In: Hazewinkel, M., Gerstenhaber, M. (eds) Deformation Theory of Algebras and Structures and Applications (Il Ciocco, 1986), NATO Advance Science Institute Series C Mathematical and Physical Sciences, vol. 247, pp.~11-264. Kluwer Academic, Dordrecht (1988) (Co)homology theory in algebraic geometry, Localization of categories, calculus of fractions, Deformations and infinitesimal methods in commutative ring theory, Associative rings of functions, subdirect products, sheaves of rings, Presheaves and sheaves, stacks, descent conditions (category-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 Valery Alexeev & Michel Brion, ''Stable reductive varieties. II. Projective case'', Adv. Math.184 (2004) no. 2, p. 380-408 Fine and coarse moduli spaces, Representation theory for linear algebraic groups, Toric varieties, Newton polyhedra, Okounkov bodies, Noncommutative algebraic geometry, 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 Hassett, B.: Some rational cubic fourfolds. J. Algebr. Geom. 8(1), 103--114 (1999) \(4\)-folds, Rational and unirational 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 Determinants, permanents, traces, other special matrix functions, Research exposition (monographs, survey articles) pertaining to linear algebra, Affine algebraic groups, hyperalgebra constructions, 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 Noncommutative algebraic geometry, Varieties and morphisms
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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 Andreas-Stephan Elsenhans and Jörg Jahnel, Cubic surfaces with a Galois invariant double-six, Cent. Eur. J. Math. 8 (2010), no. 4, 646 -- 661. Rational and ruled surfaces, Global 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 Piene R., Singularities 40 (1983) Singularities of surfaces or higher-dimensional varieties, Singularities 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 Bueso, J. L., Segura, M. I., and Verschoren, A., Strong stability and sheaves,Comm. Algebra 19 (1991), 2531-2545. Associative rings of functions, subdirect products, sheaves of rings, Local cohomology and algebraic geometry, Noetherian rings and modules (associative rings and 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 A. Gimigliano and A. Lorenzini,On the ideal of Veronesean surfaces, Can. J. Math. 45, 758--777 (1993). Rational and ruled surfaces, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal 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 Mathematics and visual arts, Rational and ruled surfaces, History of algebraic geometry, Arts, music, language, architecture (aspects of mathematics education)
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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 [9] L. Manivel. Configurations of lines and models of Lie algebras. \(J. Algebra\) 304:457-486, 2006. &MR~22 | &Zbl~1167. Exceptional (super)algebras, Rational and ruled surfaces, Steiner systems in finite geometry, Finite affine and projective planes (geometric aspects), Combinatorial structures in finite projective 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 Antieau, B.: Étale twists in noncommutative algebraic geometry and the twisted Brauer space Brauer groups of schemes, Algebraic moduli problems, moduli of vector bundles, (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, 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 Geometric constructions in real or complex geometry, Rational and ruled surfaces, Linear equations (linear algebraic aspects), Combinatorial aspects of representation theory, Enumerative problems (combinatorial problems) in algebraic geometry, Euclidean analytic 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 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 Divisors, linear systems, invertible sheaves, Rational and ruled surfaces, 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 Rational and ruled surfaces, Automorphisms of surfaces and higher-dimensional varieties, Semialgebraic sets and related 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 Kotschick, D.; Lisca, P., Instanton invariants of P\^{}\{2\} via topology, Math. Ann., 303, 345, (1995) Differential topological aspects of diffeomorphisms, Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills), 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, Sheaves in algebraic geometry, Topoi, Accessible and locally presentable categories, Grothendieck topologies and Grothendieck topoi, Monoidal categories, symmetric monoidal categories, Abelian categories, Grothendieck 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 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 \(3\)-folds, 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 Bernardi, A.; Catalisano, M. V.: Some defective secant varieties to osculating varieties of Veronese surfaces, Collect. math. 57, No. 1, 43-68 (2006) Rational and ruled surfaces, Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series, Projective techniques 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 Aprodu M., Brînzănescu V., Fibrés vectoriels de rang 2 sur les surfaces réglées, C. R. Math. Acad. Sci. Paris, 1996, 323(6), 627--630 Vector bundles on surfaces and higher-dimensional varieties, and their moduli, 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 Families, moduli, classification: algebraic theory, 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 Relativistic cosmology, String and superstring theories; other extended objects (e.g., branes) in quantum field 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 Wemyss, M., The \(\operatorname{GL}(2, \mathbb{C})\) McKay correspondence, Math. Ann., 350, 3, 631-659, (2011) Arcs and motivic integration, Rings arising from noncommutative algebraic geometry, Cohen-Macaulay modules, 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 Keilen, T.: Reducible families of curves with ordinary multiple points on surfaces in projective three-space, Comm. in algebra 34,5, 1921-1926 (2006) Families, moduli of curves (algebraic), Families, moduli of curves (analytic), Singularities of curves, local rings, 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 Alexeev, Valery; Nikulin, Viacheslav V., Del Pezzo and \(K3\) surfaces, MSJ Memoirs 15, xvi+149 pp., (2006), Mathematical Society of Japan, Tokyo Research exposition (monographs, survey articles) pertaining to algebraic geometry, \(K3\) surfaces and Enriques surfaces, 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 Orlov, D., \textit{smooth and proper noncommutative schemes and gluing of DG categories}, Adv. Math., 302, 59-105, (2016) Fundamental constructions in algebraic geometry involving higher and derived categories (homotopical algebraic geometry, derived algebraic geometry, etc.), Noncommutative algebraic geometry, Differential graded algebras and applications (associative algebraic aspects), Derived categories, triangulated categories, Derived categories of sheaves, dg categories, and related constructions in algebraic geometry, 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 Singularities of surfaces or higher-dimensional varieties, Twisted and skew group rings, crossed products, Actions of groups and semigroups; invariant theory (associative rings and 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 Rational points, Global ground 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 Vector bundles on curves and their moduli, Algebraic moduli problems, moduli of vector bundles, Rational and ruled surfaces, Parametrization (Chow and Hilbert schemes), Special divisors on curves (gonality, Brill-Noether theory), Special algebraic curves and curves of low genus
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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 J. S. Golan, ''More topologies on the torsion-theoretic spectrum of ring,''Period. Math. Hung.,21, No. 4, 257--260 (1990). Torsion theories; radicals on module categories (associative algebraic aspects), Metric spaces, metrizability, Topological lattices, 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 Duncan, A, Finite groups of essential dimension \(2\), Comment. Math. Helv., 88, 555-585, (2013) Group actions on varieties or schemes (quotients), Birational automorphisms, Cremona group and generalizations, 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 Syzygies, resolutions, complexes and commutative rings, Rational and ruled surfaces, Projective techniques 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 Vector bundles on surfaces and higher-dimensional varieties, and their moduli, 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, 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 Cirio, L.S., Landi, G., Szabo, R.J.: Algebraic deformations of toric varieties. I: general constructions. Adv. Math. \textbf{246}, 33 (2013). arXiv:1001.1242 [math.QA] Noncommutative algebraic geometry, Formal methods and deformations in algebraic geometry, Toric varieties, Newton polyhedra, Okounkov bodies
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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 Bruyn, L, Representation stacks, D-branes and noncommutative geometry, Commun. Algebra, 40, 3636-3651, (2012) Generalizations (algebraic spaces, stacks), Trace rings and invariant theory (associative rings and 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 Lubbes, N.: Families of circles on surfaces, Contributions to Algebra and Geometry, to appear. arXiv:1302.6710 Families, moduli of curves (algebraic), Rational and ruled surfaces, Toric varieties, Newton polyhedra, Okounkov bodies, Adjunction problems
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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. Bogomolov and L. Katzarkov, ''Complex projective surfaces and infinite groups,'' Geom. Funct. Anal., vol. 8, iss. 2, pp. 243-272, 1998. Homotopy theory and fundamental groups in algebraic geometry, Rational and ruled surfaces, Fundamental groups and their automorphisms (group-theoretic aspects), Coverings 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 Castorena, A.; Ciliberto, C.: On a theorem of Castelnuovo and applications to moduli, Kyoto J. Math. 51, No. 3, 633-645 (2011) Rational and ruled surfaces, Divisors, linear systems, invertible sheaves, Families, moduli of curves (algebraic)
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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 Vo, N.; Grasegger, G.; Winkler, F., Deciding the existence of rational general solutions for first-order algebraic odes, J. Symbolic Comput., 87, 127-139, (2018) Explicit solutions, first integrals of ordinary differential equations, Geometric methods in ordinary differential equations, Nonlinear ordinary differential equations and systems, Special algebraic curves and curves of low genus, 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 Diaz, H.: The motive of the Fano surface of lines, arXiv:1602.06403v1 (Equivariant) Chow groups and rings; motives, Rational and ruled surfaces, Fano 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 Deligne, P.; Lehrer, GI; Zhang, RB, The first fundamental theorem of invariant theory for the orthosymplectic super group, Adv. Math., 327, 4-24, (2018) Supervarieties, Vector and tensor algebra, theory of invariants, 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 Hypersurfaces and algebraic geometry, Rational and ruled surfaces, \(3\)-folds, \(4\)-folds, Calabi-Yau manifolds (algebro-geometric aspects), Jacobians, Prym varieties, Picard schemes, higher Jacobians, Rationality questions in algebraic geometry, Rational and unirational 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 Associative rings of functions, subdirect products, sheaves of rings, Rational and birational maps, Extensions of associative rings by ideals, Ideals in 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 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 ground 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 Ingalls, C.; Patrick, D.: Blowing up quantum weighted projective planes. J. algebra 254, 92-114 (2002) Rational and ruled surfaces, Noncommutative algebraic geometry, 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 Nyman, A, The geometry of arithmetic noncommutative projective lines, J. Algebra, 414, 190-240, (2014) Noncommutative algebraic geometry, 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 Hart, J.; Nyman, A.: Duals of simple two-sided vector spaces, Comm. algebra 40, 2405-2419 (2012) Bimodules in associative algebras, Vector spaces, linear dependence, rank, lineability, Noncommutative algebraic geometry, 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 J.~T. Stafford and M. van~den Bergh, \emph{Noncommutative curves and noncommutative surfaces}, Bull. Amer. Math. Soc. (N.S.) \textbf{38} (2001), no.~2, 171--216. \MR{1816070} Rings arising from noncommutative algebraic geometry, Noncommutative algebraic geometry, Growth rate, Gelfand-Kirillov dimension, Graded rings and modules (associative rings and 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 Nyman, A; Pappacena, CJ, Two-sided vector spaces, Linear Algebra Appl., 420, 339-360, (2007) Vector spaces, linear dependence, rank, lineability, Bimodules in associative algebras, Noncommutative algebraic geometry, \(K_0\) of other rings, Computations of higher \(K\)-theory 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 Bergh, M, Non-commutative \(\mathbb{P}^1\)-bundles over commutative schemes, Trans. Am. Math. Soc., 364, 6279-6313, (2012) Noncommutative algebraic geometry, Formal methods and deformations 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 Chan, D., Nyman, A.: Species and noncommutative \(\mathbb {P}^{1}\)'s over non-algebraic bimodules, in progress Representations of quivers and partially ordered sets, Noncommutative algebraic geometry
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Delzell C.\ N., A continuous, constructive solution to Hilbert's 17th problem, Invent. Math. 76 (1984), 365-384. Ordered fields, Forms over real fields, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), General binary quadratic forms, Forms of degree higher than two, Intuitionistic mathematics, Other constructive mathematics, Connections of number theory and logic, Topological fields, rings, etc. (topological aspects), Real algebraic and real-analytic geometry
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Xiaoshan, Gao: Mathematics mechanization: a survey. Adv. math. 30, No. 5, 385-404 (2001) Mechanization of proofs and logical operations, Effectivity, complexity and computational aspects of algebraic geometry, Learning and adaptive systems in artificial intelligence, Other constructive mathematics, Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations, Research exposition (monographs, survey articles) pertaining to algebraic geometry
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Research exposition (monographs, survey articles) pertaining to field theory, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Lombardi, H.: Effective real nullstellensatz and variants. Progress in math., no.~94, 263-288 (1991) Effectivity, complexity and computational aspects of algebraic geometry, Semialgebraic sets and related spaces, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Relevant commutative algebra, Other constructive mathematics, Real algebraic sets
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Arnon, D., Mignotte, M.: On mechanical quantifier elimination for elementary algebra and geometry. J. Symb. Comput. 5, 237--259 (1988) Symbolic computation and algebraic computation, Quantifier elimination, model completeness, and related topics, Mechanization of proofs and logical operations, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Real algebraic and real-analytic geometry
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Perrucci, D, Linear solving for sign determination, Theor. Comput. Sci., 412, 4715-4720, (2011) Symbolic computation and algebraic computation, Effectivity, complexity and computational aspects of algebraic geometry
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Basarab, Serban A.: Definite functions on algebraic varieties over ordered fields. Rev. roumaine math. Pures appl. 29, 527-535 (1984) Ordered fields, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Rational points, Real algebraic and real-analytic geometry, Model-theoretic algebra, Foundations of classical theories (including reverse mathematics)
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Ayad, A.: A survey on the complexity of solving algebraic systems. Int. Math. Forum 5(7), 333--353 (2010) Solving polynomial systems; resultants, Number-theoretic algorithms; complexity, Symbolic computation and algebraic computation, Effectivity, complexity and computational aspects of algebraic geometry, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation [4] S.-C. Chou and X.-S. Gao, \textit{Ritt-Wu's decomposition algorithm and geometry theorem proving}, Proc. 10th International Conference on Automated Deduction (M.E. Stickel, ed.), pp. 207-- 220, Springer, Berlin (1990). Projective techniques in algebraic geometry, Questions of classical algebraic geometry, Mechanization of proofs and logical operations, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Cohen, C.: Mahboubi, A.: Formal proofs in real algebraic geometry: from ordered fields to quantifier elimination. Logical Methods Comput. Sci. \textbf{8}(1:02), 1-40 (Feb 2012) https://hal.inria.fr/inria-00593738 Quantifier elimination, model completeness, and related topics, Ordered fields, Real algebraic and real-analytic geometry, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Semialgebraic sets and related spaces, Symbolic computation and algebraic computation, Quantifier elimination, model completeness, and related topics, Effectivity, complexity and computational aspects of algebraic geometry
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Schicho, J; Sevilla, D, Radical parametrization of trigonal curves, Contemp. Math., 572, 221-231, (2012) Computational aspects of algebraic curves, Special divisors on curves (gonality, Brill-Noether theory), Symbolic computation and algebraic computation, Lie algebras of linear algebraic groups, Effectivity, complexity and computational aspects of algebraic geometry
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Brown, R.: The behaviour of chains of orderings under field extensions and places. Pacific J. Math. 127, 281-297 (1987) Ordered fields, Real algebraic and real-analytic geometry, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Non-Archimedean valued fields
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Effectivity, complexity and computational aspects of algebraic geometry, Semialgebraic sets and related spaces, Symbolic computation and algebraic computation
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Semialgebraic sets and related spaces, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Computational homological algebra, Syzygies, resolutions, complexes and commutative rings, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Lombardi, H., Yengui, I.: Suslin's algorithms for reduction of unimodular rows. J. Symb. Comput. 39, 707--717 (2005) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Other constructive mathematics, Stability for projective modules, Effectivity, complexity and computational aspects of algebraic geometry
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Computational methods for problems pertaining to field theory, Field arithmetic, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Geometric invariant theory, Effectivity, complexity and computational aspects of algebraic geometry, Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.), Symbolic computation and algebraic computation
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation D'alfonso, L.; Jeronimo, G.; Ollivier, F.; Sedoglavic, A.; Solernó, P.: A geometric index reduction method for implicit systems of differential algebraic equations, J. symb. Comput. 46, No. 10, 1114-1138 (2011) Implicit ordinary differential equations, differential-algebraic equations, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation, Transformation and reduction of ordinary differential equations and systems, normal forms
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Safey El Din, M.; Spaenlehauer, P. J., Critical point computations on smooth varieties: Degree and complexity bounds, 183-190, (2016) Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Effectivity, complexity and computational aspects of algebraic geometry, de Rham cohomology and algebraic geometry, Symbolic computation and algebraic computation, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Symbolic computation and algebraic computation, Parametrization (Chow and Hilbert schemes), Effectivity, complexity and computational aspects of algebraic geometry
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation G. Jeronimo and J. Sabia, ''Effective equidimensional decomposition of affine varieties,'' J. Pure Appl. Algebra, 169, Nos. 2--3, 229--248 (2002). Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Research exposition (monographs, survey articles) pertaining to real functions, Research exposition (monographs, survey articles) pertaining to computer science, Inequalities for trigonometric functions and polynomials, Mechanization of proofs and logical operations, Semialgebraic sets and related spaces, Symbolic computation and algebraic computation
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Effectivity, complexity and computational aspects of algebraic geometry, Semialgebraic sets and related spaces, Symbolic computation and algebraic computation
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Polynomials in real and complex fields: location of zeros (algebraic theorems), Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Skew fields, division rings, Symbolic computation and algebraic computation, Effectivity, complexity and computational aspects of algebraic geometry
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Marshall, M.: Separating families for semi-algebraic sets. Manuscripta math. 80, 73-79 (1993) Semialgebraic sets and related spaces, Real-analytic and semi-analytic sets, Ordered fields, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Monceur, S.; Yengui, I., On the leading terms ideal of polynomial ideal over a valuation ring, J. algebra, 351, 382-389, (2012) Projective and free modules and ideals in commutative rings, Stability for projective modules, Effectivity, complexity and computational aspects of algebraic geometry, Other constructive mathematics
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Sendra, J. Rafael; Villarino, Carlos, Algebraically optimal parametrizations of quasi-polynomial algebraic curves, J. Algebra Appl., 0219-4988, 1, 1, 51-74, (2002) Computational aspects of algebraic curves, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation, Toeplitz operators, Hankel operators, Wiener-Hopf operators, Toeplitz, Cauchy, and related matrices
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Recio, T; Sendra, JR; Tabera, LF; Villarino, C, Algoritmic detection of hypercircles, Math. Comput. Simul., 82, 54-67, (2011) Computational aspects of higher-dimensional varieties, Effectivity, complexity and computational aspects of algebraic geometry, Numerical aspects of computer graphics, image analysis, and computational geometry, Symbolic computation and algebraic computation
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Projective and free modules and ideals in commutative rings, Stability for projective modules, Effectivity, complexity and computational aspects of algebraic geometry, Other constructive mathematics
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Gonzalez-Vega, L.; Gonzalez-Campos, N.: Simultaneous elimination by using several tools from real algebraic geometry. J. symb. Comput. 28, 89-103 (1999) Effectivity, complexity and computational aspects of algebraic geometry, Numerical computation of solutions to systems of equations, Real algebraic and real-analytic geometry, Polynomial rings and ideals; rings of integer-valued polynomials, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Symbolic computation and algebraic computation, Computer science aspects of computer-aided design
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation [4] Caboara M., Kreuzer M., Robbiano L., ''Efficiently computing minimal sets of critical pairs'', J. of Symbolic Computation, 38:4 (2004), 1169--1190 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation
| 0
|
Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Solving polynomial systems; resultants, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation
| 0
|
Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Effectivity, complexity and computational aspects of algebraic geometry, Computational aspects of higher-dimensional varieties, Symbolic computation and algebraic computation
| 0
|
Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation, Quantifier elimination, model completeness, and related topics
| 0
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