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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 Mignon, T., Courbes lisses sur les surfaces rationnelles génériques: Un lemme d'Horace différentiel, Ann. Inst. Fourier (Grenoble), 50, 6, 1709-1744, (2000) Rational and ruled surfaces, Plane and space curves, Configurations and arrangements of linear subspaces
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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, 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 Noncommutative algebraic geometry, Formal methods and deformations in algebraic geometry, Monodromy; relations with differential equations and \(D\)-modules (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 Komeda, J., Ohbuchi, A.: Weierstrass points with first non-gap four on a double covering of a hyperelliptic curve II. Serdica Math. J. \textbf{34}, 771-782 (2008) Riemann surfaces; Weierstrass points; gap sequences, Coverings of curves, fundamental group, 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 Borowiec A., Adv. Math. 115 pp 250-- (1995) Deformations of associative rings, Quantum groups (quantized enveloping algebras) and related deformations, Rings of differential operators (associative algebraic aspects), Graded rings and modules (associative rings and algebras), Noncommutative algebraic geometry, Quantum groups and related algebraic methods applied to problems in quantum theory, Pseudogroups and differentiable groupoids, \(p\)-adic cohomology, crystalline cohomology
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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 Bowne-Anderson, H.: The explicit construction of orders on surfaces, (2011) Noncommutative algebraic geometry, Calabi-Yau manifolds (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 DOI: 10.4171/JNCG/136 Noncommutative algebraic geometry, Pencils, nets, webs in algebraic geometry, Picard 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 Noncommutative algebraic geometry, Classical or axiomatic geometry and physics, Applications of local differential geometry to the sciences
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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 Cohen-Macaulay modules, Derived categories of sheaves, dg categories, and related constructions in algebraic geometry, Syzygies, resolutions, complexes and commutative rings, Vector bundles on curves and their moduli, Plane and space curves, Noncommutative algebraic geometry, Vector bundles on curves and their moduli, Elliptic curves
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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 Etingof, P.; Oblomkov, A.; Rains, E., \textit{generalized double affine Hecke algebras of rank 1 and quantized del Pezzo surfaces}, Adv. Math., 212, 749-796, (2007) Noncommutative algebraic geometry, Quantum groups (quantized enveloping algebras) and related deformations, Hecke algebras and their representations
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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. Calaque, C. Rosso, and M. Van den Bergh, Hochschild (co)homology for Lie algebroids. Internat. Math. Res. Notices 2010 (2010), No. 21, 4098--4136. Noncommutative algebraic geometry, Connections (general 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 Diaconescu, D-E; Florea, B., The ruled vertex and nontoric del Pezzo surfaces, JHEP, 12, 028, (2006) Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), Rational and ruled surfaces, Topological field theories in quantum mechanics
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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 of curves (algebraic), Syzygies, resolutions, complexes and commutative rings, Algebraic moduli problems, moduli of vector bundles, Special divisors on curves (gonality, Brill-Noether theory), Families, moduli, classification: algebraic theory, Rational and ruled surfaces, \(K3\) surfaces and Enriques surfaces, Jacobians, Prym 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 N. Romanovskii, ''Algebraic sets in metabelian groups,'' Algebra Logic, 46, No. 4, 274--280 (2007). Solvable groups, supersolvable groups, Free nonabelian groups, Quasivarieties and varieties of groups, Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations, Noncommutative algebraic geometry, Model-theoretic algebra
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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 Tan, S.-L.: On the invariants of base changes of pencils of curves, I. Manuscripta Math.84 (1994), 225--244 Singularities of surfaces or higher-dimensional varieties, Singularities of curves, local rings, Families, fibrations 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 Real algebraic and real-analytic geometry, Noncommutative algebraic geometry, Algebras of unbounded operators; partial algebras of operators, Ordered rings, Ordered fields, Rings with involution; Lie, Jordan and other nonassociative structures
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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 Enumerative problems (combinatorial problems) in algebraic geometry, Rational and ruled surfaces, Real algebraic 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 Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Automorphisms and endomorphisms, \(T\)-ideals, identities, varieties of associative rings and algebras, Jacobian 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 Brüstle, T.; Hille, L.: Actions of parabolic subgroups in gln on unipotent normal subgroups and quasi-hereditary algebras. Coll. math. 83, 281-294 (2000) Representations of quivers and partially ordered sets, Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc., Group actions on varieties or schemes (quotients), Module categories in associative algebras, 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 Rational and ruled surfaces, Pencils, nets, webs in algebraic geometry, Elliptic curves
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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 Lutz Hille & Markus Perling, ``Tilting bundles on rational surfaces and quasi-hereditary algebras'', Ann. Inst. Fourier64 (2014) no. 2, p. 625-644 Rational and ruled surfaces, 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 Graded rings, Graded rings and modules (associative rings and algebras), Module categories in associative algebras, Rings arising from noncommutative algebraic geometry, Curves 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 Complex-analytic moduli problems, Deformations of complex structures, Families, moduli of curves (analytic), Rational and ruled surfaces, Compact complex surfaces, Surfaces of general type
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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, Structure of families (Picard-Lefschetz, monodromy, etc.), Rational and ruled surfaces, Grothendieck groups (category-theoretic aspects), Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category, Symplectic and contact topology in high or arbitrary dimension
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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, 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 Derenthal, U., Universal torsors of del Pezzo surfaces and homogeneous spaces, Adv. Math., 213, 849-864, (2007) Rational and ruled surfaces, Group actions on varieties or schemes (quotients)
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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. Wess, \textit{Deformed coordinate spaces: derivatives}, in \textit{Proceedings BW}2003 \textit{workshop, Vrnjacka Banja, Serbia and Montenegro}, G. Djordjevic, L. Nesic and J. Wess eds., World Scientific Singapore, (2005) [ISBN:9789812561305 (Print), 9789814481137 (Online)] [hep-th/0408080] [INSPIRE]. Local deformation theory, Artin approximation, etc., Bimodules in associative algebras, Drinfel'd modules; higher-dimensional motives, etc., Noncommutative algebraic geometry, Hopf algebras and their applications
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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 of schemes, 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 Counting solutions of Diophantine equations, Diophantine equations in many variables, Applications of the Hardy-Littlewood method, Rational points, 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 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 Andreas-Stephan Elsenhans & Jörg Jahnel, ``Cubic surfaces violating the Hasse principle are Zariski dense in the moduli scheme'', Adv. Math.280 (2015), p. 360-378 Varieties over global fields, Global ground fields in algebraic geometry, Rational points, Rational and ruled surfaces, 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 Tabuada, Gonçalo, \(\mathbb{A}^1\)-homotopy invariance of algebraic \(K\)-theory with coefficients and du Val singularities, Ann. K-Theory, 2, 1, 1-25, (2017) Noncommutative algebraic geometry, Singularities of curves, local rings, \(K\)-theory of schemes, Klein surfaces, Witt vectors and related 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 Clifford algebras, spinors, ``Super'' (or ``skew'') structure, Graded rings and modules (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 Fischer, G., Piontkowski, J.: \textit{Ruled Varieties, An Introduction to Algebraic Differential Geometry}. Advanced Lectures in Math., Friedr. Vieweg & Sohn, Hamburg (2001) Rational and ruled surfaces, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to differential geometry, 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 Hubert Flenner, Shulim Kaliman & Mikhail Zaidenberg, Birational transformations of weighted graphs, Affine algebraic geometry, Osaka Univ. Press, Osaka, 2007, p. 107â147 Automorphisms of surfaces and higher-dimensional varieties, Rational and ruled surfaces, Affine geometry, Graph 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 Divisors, linear systems, invertible sheaves, 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 M. Abe, M. Furushima, andT. Shima, Analytic compactifications of /\(\mathbb{Z}\)n.Abh. Math. Sem. Univ. Hamburg 74 (2004), 223--235. Compactification of analytic spaces, Rational and ruled surfaces, Compact complex 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 7. I. Gordon, Rational Cherednik algebras, in Proc. Int. Cong. Mathematicians, Vol. III, (Hindustan Book Agency, New Delhi, 2010), pp. 1209-1225. Representations of orders, lattices, algebras over commutative rings, Associative rings and algebras arising under various constructions, Lie algebras and Lie superalgebras, Noncommutative algebraic geometry, Hecke algebras and their representations, Reflection and Coxeter groups (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 Rigidity results, Noncommutative algebraic geometry, (Equivariant) Chow groups and rings; motives, Motivic cohomology; motivic homotopy theory, Enriched categories (over closed or monoidal categories), \(K\)-theory and homology; cyclic homology and cohomology
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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 Cazzaniga, A., Morrison, A., Pym, B., Szendroi, B.: Motivic Donaldson-Thomas invariants of some quantized threefolds. arXiv:1510.08116 Noncommutative algebraic geometry, Calabi-Yau manifolds (algebro-geometric aspects), Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), 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 Jørgensen, P., Finite Cohen-Macaulay type and smooth non-commutative schemes, Canad. J. Math., 60, 379-390, (2008) Noncommutative algebraic geometry, Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.), 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 Structure of families (Picard-Lefschetz, monodromy, etc.), 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 Rational and ruled surfaces, Singularities of 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 Rigid analytic geometry, Modular and Shimura varieties, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, Rings arising from noncommutative algebraic geometry, Representations of Lie and linear algebraic groups over local 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 Applications of global analysis to structures on manifolds, Rational and ruled surfaces, Symplectic manifolds (general theory), Differentiable structures in differential topology
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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 10.1017/is010011013jkt134 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 A. Polishchuk, Noncommutative proj and coherent algebras. Math. Res. Lett. 12 (2005), 63-74. 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 Addington, N., Aspinwall, P.S.: Categories of massless D-branes and del Pezzo surfaces. J. High Energy Phys. \textbf{7}, 176 (2013) String and superstring theories in gravitational theory, Relationships between surfaces, higher-dimensional varieties, and physics, 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 Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects), Noncommutative algebraic geometry, Noncommutative differential geometry, Noncommutative topology
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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 Guth, L.: Ruled surface theory and incidence geometry. arXiv:1606.07682 (2016) Rational and ruled surfaces, Erdős problems and related topics of discrete geometry, Linear incidence 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 Failla G., Lahyane M., Molica Bisci G.: The finite generation of the monoid of effective divisor classes on Platonic rational surfaces, pp. 565--576. World Sci. Publ., Hackensack (2007) 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 Yekutieli, A., Zhang, J.J.: Rigid complexes via DG algebras. Trans. AMS 360, 3211--3248 (2008) Resolutions; derived functors (category-theoretic aspects), Differential graded algebras and applications (associative algebraic aspects), Ext and Tor, generalizations, Künneth formula (category-theoretic aspects), 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 Russo, F, On a theorem of Severi, Math. Ann., 316, 1-17, (2000) 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 Noncommutative geometry (à la Connes), Other ``noncommutative'' mathematics based on \(C^*\)-algebra theory, Noncommutative algebraic geometry, Operations and obstructions in algebraic topology
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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 Classification of affine varieties, Rational and ruled surfaces, General low-dimensional topology, Surgery and handlebodies
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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 and free modules and ideals in commutative rings, Ideals in associative algebras, Noncommutative algebraic geometry, 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 García, Luis Fuentes, Seshadri constants on ruled surfaces: the rational and the elliptic cases, Manuscripta Math., 119, 4, 483-505, (2006) 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 F. Mangolte, Real algebraic morphisms on 2-dimensional conic bundles, Adv. Geom., to appear. Zbl1097.14045 MR2243296 Real algebraic sets, Topology of real algebraic 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 Daniyarova, È. Yu.; Remeslennikov, V. N., Bounded algebraic geometry over a free Lie algebra, Algebra Logika. Algebra Logic, 44 44, 3, 148-167, (2005) Identities, free Lie (super)algebras, Noncommutative algebraic geometry, Lie (super)algebras associated with other structures (associative, Jordan, 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 Savchuk, Y.; Schmüdgen, K.: A noncommutative version of the Fejér-Riesz theorem, Proc. amer. Math. soc. 138, No. 4, 1243-1248 (2010) Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators, Noncommutative algebraic geometry, Trigonometric polynomials, inequalities, extremal problems, Linear operators in \({}^*\)-algebras, Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, 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 Riemann surfaces; Weierstrass points; gap sequences, Coverings of curves, fundamental group, 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 Tabuada, G.: \textit{E}\_{}\{\textit{n}\}-regularity implies \textit{E}\_{}\{\textit{n}\(-\)1\}-regularity. Documenta Math. 19, 121-139 (2014) Noncommutative algebraic geometry, Applications of methods of algebraic \(K\)-theory 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 Hausen, J.; Süß, H., The Cox ring of an algebraic variety with torus action, Adv. Math., 225, 977-1012, (2010) Divisors, linear systems, invertible sheaves, Toric varieties, Newton polyhedra, Okounkov bodies, 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 W. Lee and E. Park, On non-normal del Pezzo varieties. J. Algebra 387 (2013), 11-28 Projective techniques in algebraic geometry, Varieties of low degree, 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 Pierrette Cassou-Noguès and Peter Russell, Birational morphisms \Bbb C²\to \Bbb C² and affine ruled surfaces, Affine algebraic geometry, Osaka Univ. Press, Osaka, 2007, pp. 57 -- 105. Birational automorphisms, Cremona group and generalizations, Rational and ruled surfaces, 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 M Friedman, M Teicher, On the fundamental group related to the Hirzebruch surface \(F_1\) Coverings of curves, fundamental group, Embeddings in algebraic geometry, Homotopy theory and fundamental groups 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 Elagin [Elagin 07] A. D., Math. Notes 82 pp 33-- (2007) 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 Division rings and semisimple Artin rings, Vector and tensor algebra, theory of invariants, Rings with polynomial identity, Endomorphism rings; matrix rings, Arithmetic theory of algebraic function fields, 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 Brian Harbourne, ``Global aspects of the geometry of surfaces'', Ann. Univ. Paedagog. Crac. Stud. Math.9 (2010), p. 5-41 Divisors, linear systems, invertible sheaves, Rational and ruled surfaces, Structure, classification theorems for modules and ideals in 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 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 Determinants, permanents, traces, other special matrix functions, Length, area and volume in real or complex geometry, Integration of real functions of several variables: length, area, volume, Three-dimensional polytopes, Euclidean analytic geometry, Rational and ruled surfaces, Plane and space curves
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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 Yoshioka, Kōta, The Picard group of the moduli space of stable sheaves on a ruled surface, J. Math. Kyoto Univ., 36, 2, 279-309, (1996) Picard groups, 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 G. MARTENS, The gonality of curves on a Hirzebruch surface, Arch. Math., 67 (1996), pp. 349-352. Zbl0872.14022 MR1407339 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 M.-H. SAITO - V. NGUYEN KHAC, On Mordell-Weil lattices for nonhyperelliptic fibrations of surfaces with zero geometric genus and irregularity, Izv. Ross. Akad. Nauk Ser. Mat., 66 (2002), pp. 137-154. Zbl1053.14043 MR1942097 Rational and ruled surfaces, Families, moduli of curves (algebraic), 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 Manin, Y. I., Quantized theta-functions, \textit{Progress of theoretical physics. Supplement}, 102, 219-228, (1991) Noncommutative algebraic geometry, Theta functions and abelian varieties, Quantum groups (quantized enveloping algebras) and related deformations, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics, Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie 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 Free semigroups, generators and relations, word problems, Noncommutative algebraic geometry, Algebraic geometry over groups; equations over 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 Ring geometry (Hjelmslev, Barbilian, etc.), Questions of classical algebraic geometry, Noncommutative algebraic geometry, Noncommutative local and semilocal rings, perfect 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, Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.), Graded rings and modules (associative rings and algebras), Centralizing and normalizing extensions
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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. Van de Weyer, Double Poisson structures on finite dimensional semi-simple algebras, math.AG/0603533. 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 Research exposition (monographs, survey articles) pertaining to associative rings and algebras, Research exposition (monographs, survey articles) pertaining to nonassociative rings and algebras, Research exposition (monographs, survey articles) pertaining to group theory, Noncommutative algebraic geometry, Hopf algebras and their applications, Bialgebras, Ring-theoretic aspects of quantum groups, Yang-Baxter equations, Quantum groups (quantized enveloping algebras) and related deformations, Quantum groups and related algebraic methods applied to problems in quantum theory, Noncommutative geometry in quantum 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 Miranda, R, Bi-elliptic surface as coverings of rational surfaces, Advances in Math., 198, 439-447, (2005) Special surfaces, Rational and ruled surfaces, Elliptic surfaces, elliptic or Calabi-Yau 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 Noncommutative topology, Noncommutative differential geometry, Noncommutative algebraic geometry, Special relativity
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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. Iyama and M. Wemyss, Maximal modifications and Auslander-Reiten duality for non-isolated singularities, Invent. Math. 197 (2014), no. 3, 521-586. Noncommutative algebraic geometry, Representations of quivers and partially ordered sets, Local theory 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 Blanc, A., \textit{topological K-theory of complex noncommutative spaces}, Compos. Math., 152, 489-555, (2016) Noncommutative algebraic geometry, \(K\)-theory and homology; cyclic homology and cohomology
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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 Structure of families (Picard-Lefschetz, monodromy, etc.), Rational and unirational varieties, Families, moduli, classification: algebraic theory, Rational and ruled surfaces, Rational and birational maps, Singularities of surfaces or higher-dimensional varieties, Normal analytic 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 Kähler-Einstein manifolds, Notions of stability for complex manifolds, Fano varieties, Rational and ruled surfaces, Kähler 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 C. K. Gupta and N. S. Romanovskii, ''The property of being equationally Noetherian for some soluble groups,'' Algebra Logic, 46, No. 1, 28--36 (2007). Solvable groups, supersolvable groups, Extensions, wreath products, and other compositions of groups, Quasivarieties and varieties of groups, 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 Algebraic moduli problems, moduli of vector bundles, Vector bundles on surfaces and higher-dimensional varieties, and their moduli, Rational and ruled surfaces, Rationality questions 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, Vector bundles on surfaces and higher-dimensional varieties, and their moduli, 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 Nilpotent groups, Free nonabelian groups, Quasivarieties and varieties of groups, Noncommutative algebraic geometry, Graphs and abstract algebra (groups, rings, fields, etc.), Generators, relations, and presentations of groups, Braid groups; Artin 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 Modular and Shimura varieties, Representations of Lie and linear algebraic groups over local fields, Rigid analytic geometry, Local ground fields in algebraic geometry, 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
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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 Zilber, A class of quantum zariski geometries, in: Model theory with applications to algebra and analysis I (2008) Models of other mathematical theories, Model-theoretic algebra, Noncommutative algebraic geometry, Quantum groups and related algebraic methods applied to problems in quantum 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 Noncommutative algebraic geometry, Torelli problem, Rationality questions in algebraic geometry, \(3\)-folds, Fano varieties, Picard schemes, higher Jacobians
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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, Cohen-Macaulay modules, 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 Colombo, E.; van Geemen, B.; Looienga, E., Del Pezzo moduli via root systems, (Algebra, arithmetic, and geometry: in honor of yu.I. Manin. vol. I, Progr. math., vol. 269, (2009), Birkhäuser Boston, Inc. Boston, MA), 291-337 Families, moduli, classification: algebraic theory, Rational and ruled surfaces, Simple, semisimple, reductive (super)algebras, Classical problems, Schubert 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 Flenner H., Kaliman S., Zaidenberg M.: On the Danilov-Gizatullin isomorphism theorem. Enseignement Mathématiques 55(2), 1--9 (2009) Rational and ruled surfaces, Classification of 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 Singh, B; Shukla, G; Kundu, D, Spatio-temporal models in small area estimation, Surv Methodol, 31, 183-195, (2005) Rational and ruled surfaces, (Equivariant) Chow groups and rings; motives, Arithmetic ground fields for surfaces or higher-dimensional varieties, Varieties over finite and local 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 Dohm, M, Implicitization of rational ruled surfaces with \(\mu\)-bases, Journal of Symbolic Computation, 44, 479-489, (2009) Computational aspects of algebraic surfaces, Rational and ruled surfaces
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