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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces S. P. Smith and J. J. Zhang,Curves on quasi-schemes, Algebras and Representation Theory1 (1998), 311--351. Graded rings and modules (associative rings and algebras), Homological dimension in associative algebras, Special algebraic curves and curves of low genus, Relationships between algebraic curves and physics, \(K_0\) of other rings, Rings arising from noncommutative algebraic geometry, Quantum groups (quantized enveloping algebras) and related deformations
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal 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
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal 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 in associative algebras, Homological dimension and commutative rings, Noncommutative algebraic geometry
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Gurjar, RV; Pradeep, CR; Shastri, AR, On rationality of logarithmic \({\mathbb{Q}}\)-homology planes. II, Osaka J. Math., 34, 725-743, (1997) Rational and ruled surfaces, Classical real and complex (co)homology 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 P. Putrov, J. Song and W. Yan, (0\(,\) 4) \textit{dualities}, \textit{JHEP}\textbf{03} (2016) 185 [arXiv:1505.07110] [INSPIRE]. Calabi-Yau manifolds (algebro-geometric aspects), Gromov-Witten invariants, quantum cohomology, Frobenius manifolds, Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), Topological field theories in quantum mechanics, Rational and ruled surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative algebraic geometry, Topological and ordered rings and modules, Equational classes, universal algebra in model 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 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 Nuer, H., Unirationality of moduli spaces of special cubic fourfolds and \textit{K}3 surfaces, Algebraic geom., 4, 281-289, (2017) Parametrization (Chow and Hilbert schemes), Variation of Hodge structures (algebro-geometric aspects), Algebraic moduli problems, moduli of vector bundles, Rational and ruled surfaces, \(K3\) surfaces and Enriques surfaces, Rational and birational maps
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Poisson algebras, Ordinary and skew polynomial rings and semigroup rings, Chain conditions, growth conditions, and other forms of finiteness for associative rings and algebras, Automorphisms and endomorphisms, Rings arising from noncommutative algebraic geometry, Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Derivations, actions of 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 J. Cuntz, ''Cycle Homology and Nonsingularity,'' J. AMS 8(2), 373--442 (1995). \(K\)-theory and homology; cyclic homology and cohomology, Noncommutative algebraic geometry, Noncommutative topology, Noncommutative differential geometry, Riemann-Roch theorems, Chern characters, de Rham cohomology 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 Fano varieties, Kähler-Einstein manifolds, Rational and ruled surfaces, Computational aspects of algebraic surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Okoh, F.; Zorzitto, F. A.: Curves arising from Kronecker modules. Linear algebra appl. 365, 311-348 (2003) Endomorphism rings; matrix rings, Plane and space curves, Birational automorphisms, Cremona group and generalizations
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces 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 Fioresi, R.; Kwok, S. D.; Gorelik, M. (ed.); Papi, P. (ed.), On SUSY curves, (2014) Analysis on supermanifolds or graded manifolds, Finite-dimensional groups and algebras motivated by physics and their representations, Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations, Supervarieties, Noncommutative algebraic geometry, Supermanifolds and graded manifolds
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Gonçalo Tabuada, On Drinfeld's dg quotient, J. Algebra 323 (2010), no. 5, 1226 -- 1240. Noncommutative algebraic geometry, Categorical 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 Derived categories of sheaves, dg categories, and related constructions in algebraic geometry, Noncommutative algebraic geometry, Derived categories and associative algebras, Derived categories and 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 R. Blache. Positivity Results for Euler Characteristics of Singular Surfaces.Math. Z. 215 (1994), 1--12. Singularities of surfaces or higher-dimensional varieties, Topological properties 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 Andreas-Stephan Elsenhans and Jörg Jahnel, On the order three Brauer classes for cubic surfaces, Cent. Eur. J. Math. 10 (2012), no. 3, 903 -- 926. Varieties over global fields, Brauer groups of schemes, 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 Surfaces in Euclidean and related spaces, Rational and ruled surfaces, Curves in Euclidean 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 Z. Sela, ''Diophantine Geometry over Groups. IV: An Iterative Procedure for Validation of a Sentence,'' Isr. J. Math. 143, 1--130 (2004). Word problems, other decision problems, connections with logic and automata (group-theoretic aspects), Free nonabelian groups, Quasivarieties and varieties of groups, Applications of logic to group theory, Diophantine equations in many variables, Noncommutative algebraic geometry, Decidability of theories and sets of sentences, Basic properties of first-order languages and structures, 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 K. Yoshioka, \textit{Euler characteristics of} SU(2) \textit{instanton moduli spaces on rational elliptic surfaces}, \textit{Commun. Math. Phys.}\textbf{205} (1999) 501 [math/9805003] [INSPIRE]. Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory), Rational and ruled surfaces, Families, moduli, classification: algebraic theory, Elliptic surfaces, elliptic or Calabi-Yau fibrations, Topological properties in algebraic geometry, Relationships between surfaces, higher-dimensional varieties, and physics
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces H. Kojima, Minimal singular compactifications of the affine plane. Nihonkai Math. J. 12(2), 165-195 (2001) Singularities of surfaces or higher-dimensional varieties, Rational and ruled surfaces, Complex surface and hypersurface singularities, Compactification of 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 Kollár, J., Rational Curves on Algebraic Varieties, (1995), Springer: Springer Berlin Minimal model program (Mori theory, extremal rays), Rational and ruled surfaces, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Parametrization (Chow and Hilbert schemes), Fano varieties, Rational and unirational varieties, Riemann-Roch theorems, Families, moduli of curves (algebraic), 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 Proceedings, conferences, collections, etc. pertaining to associative rings and algebras, Representation theory of associative rings and algebras, Modular representations and characters, Noncommutative algebraic geometry, Proceedings of conferences of miscellaneous specific interest
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Geometric methods (including applications of algebraic geometry) applied to coding theory, Applications to coding theory and cryptography of arithmetic geometry, Rational and ruled surfaces, Algebraic coding theory; cryptography (number-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 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, Commutative rings of differential operators and their modules, Rings arising from noncommutative algebraic geometry, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Rational and ruled surfaces, Complete intersections
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Polishchuk, A.; Vaintrob, A., \textit{Chern characters and Hirzebruch-Riemann-Roch formula for matrix factorizations}, Duke Math. J., 161, 1863-1926, (2012) Noncommutative algebraic geometry, Singularities in algebraic geometry, Complex surface and hypersurface singularities
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal 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. -H. Lee: Gosset polytopes in Picard groups of del Pezzo surfaces. Can. J. Math. 64 (2012), 123--150. Rational and ruled surfaces, Lie groups, Reflection groups, reflection geometries
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Surfaces and higher-dimensional varieties, Projective and enumerative algebraic geometry, Global differential geometry, Symplectic geometry, contact geometry, General low-dimensional topology, Differential topology, Rational and ruled surfaces, Surfaces of general type, Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), Real algebraic and real-analytic geometry, Almost complex manifolds, General geometric structures on manifolds (almost complex, almost product structures, etc.), Symplectic aspects of Floer homology and cohomology, General geometric structures on low-dimensional manifolds, Specialized structures on manifolds (spin manifolds, framed manifolds, etc.), Symplectic and contact topology in high or arbitrary dimension, Differentiable structures in differential topology, Applications of global analysis to structures on manifolds, Floer homology, Collections of abstracts of lectures
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal 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, Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product), General theory of \(C^*\)-algebras, Loop groups and related constructions, group-theoretic treatment, Topology of vector bundles and fiber 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 Research exposition (monographs, survey articles) pertaining to algebraic geometry, 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 Choi, Y.; Park, E., On higher syzygies of ruled surfaces III, J. pure appl. algebra, 219, 4653-4666, (2015) 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 \(K3\) surfaces and Enriques surfaces, Brauer groups of schemes, Arithmetic ground fields for surfaces or higher-dimensional varieties, Rational and ruled surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces 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 Automorphisms of surfaces and higher-dimensional varieties, Topology of real algebraic varieties, Rational and ruled surfaces, \(K3\) surfaces and Enriques surfaces, Birational automorphisms, Cremona group and generalizations, 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 T. Shioda, Arithmetic and geometry of Fermat curves, In: Algebraic Geometry Seminar, Singapore, 1987, World Sci. Publishing, Singapore, 1988, pp. 95-102. Automorphisms of surfaces and higher-dimensional varieties, 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 Vector bundles on surfaces and higher-dimensional varieties, and their moduli, Rational and ruled surfaces, Algebraic moduli problems, moduli of vector bundles
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces C. Tu, W. Wang, B. Mourrain and J. Wang, \textit{Signature sequence of intersection curve of two quadrics for exact morphological classification}, preprint, available at http://arxiv.org/abs/cs/0701121. Research exposition (monographs, survey articles) pertaining to algebraic geometry, Varieties over global fields, Arithmetic ground fields for surfaces or higher-dimensional varieties, Elliptic surfaces, elliptic or Calabi-Yau fibrations, Rational and ruled surfaces, Cubic and quartic Diophantine equations, Global ground fields in algebraic geometry, Arithmetic ground fields (finite, local, global) and families or 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 Fontanari, C.: Towards Bounded Negativity of Self-Intersection on General Blownup Projective Planes. Comm. Alg. 40 (2012), 1762--1765. Formal methods and deformations in algebraic geometry, Plane and space curves, Rational and ruled surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Degtyarev, A.; Itenberg, I.; Zvonilov, V., Real trigonal curves and real elliptic surfaces of type I, \textit{J. Reine Angew. Math}.,, \textbf{686}, 221-246, (2014) Topology of real algebraic varieties, Families, moduli of curves (algebraic), Dessins d'enfants theory, 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 Rational and ruled surfaces, Other special types of 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 U. PERSSON, Genus two fibration revisited, Complex algebraic varieties (Bayreuth, 1990), 133-144, Lec ture Notes in Math. 1507, Springer-Verlag, Berlin, 1992. Rational and ruled surfaces, Structure of families (Picard-Lefschetz, monodromy, etc.), Characteristic classes and numbers 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 Rings with polynomial identity, (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.), Graded rings and modules (associative rings and algebras), Endomorphism rings; matrix rings, Applications of methods of algebraic \(K\)-theory in algebraic geometry, Clifford algebras, spinors
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal 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. Shevlyakov, ''On disjunctions of equations over semigroups,'' arXiv:1305.6842. Free semigroups, generators and relations, word problems, Algebraic geometry over groups; equations over groups, Noncommutative algebraic geometry, Algebraic monoids
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal 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.: Rational surfaces of Kodaira type \textit{IV}\ . Boll. Unione Mat. Ital., Sezione B. (8) 10(3), 741-750 (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 DOI: 10.1080/00927872.2012.749884 Rational and ruled surfaces, Rational and birational maps, 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 M. Akhtar, T. Coates, A. Corti, L. Heuberger, A. Kasprzyk, A. Oneto, A. Petracci, T. Prince, K. Tveiten, Mirror symmetry and the classification of orbifold del Pezzo surfaces. \textit{Proc. Amer. Math. Soc}. \textbf{144} (2016), 513-527. MR3430830 Zbl 06548665 Mirror symmetry (algebro-geometric aspects), Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry), Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), 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 Harrison, M.C.: Explicit solution by radicals, gonal maps and plane models of algebraic curves of genus 5 or 6, preprint arXiv:1103.4946 (2011) Special divisors on curves (gonality, Brill-Noether theory), Rational and ruled surfaces, 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 Curves in Euclidean and related spaces, Surfaces in Euclidean and related spaces, Rational and ruled surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces A.N. Zubkov.: Endomorphisms of tensor products of exterior powers and Procesi hypothesis. Commun. Algebra 22, 6385--6399 (1994) Representation theory for linear algebraic groups, Endomorphism rings; matrix rings, Combinatorial aspects of representation theory, Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics, Geometric invariant 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, G., \(\mathbb{A}^1\)-homotopy invariants of dg orbit categories, J. algebra, 434, 169-192, (2015) Cluster algebras, Noncommutative algebraic geometry, Vector bundles on surfaces and higher-dimensional varieties, and their moduli, Karoubi-Villamayor-Gersten \(K\)-theory, Negative \(K\)-theory, NK and Nil, \(K\)-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 Real algebraic sets, Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), 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 Brauer groups (algebraic aspects), Noncommutative algebraic geometry, Brauer groups of schemes, Grothendieck groups, \(K\)-theory, etc., Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.), Enriched categories (over closed or monoidal categories), \(K_2\) and the Brauer group, Singularities of curves, local 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 DOI: 10.1007/s12188-009-0031-2 Spin and Spin\({}^c\) geometry, Lie algebras of vector fields and related (super) algebras, Supermanifolds and graded manifolds, Differential geometry of homogeneous manifolds, Noncommutative algebraic geometry, Supervarieties, Complex supergeometry
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal 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 and modules (associative rings and algebras), Universal enveloping (super)algebras, Noncommutative algebraic geometry
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Rational and birational maps, Minimal model program (Mori theory, extremal rays), 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 Noncommutative algebraic geometry, Singularities in algebraic geometry, Differential graded algebras and applications (associative algebraic aspects), (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.), Complex surface and hypersurface singularities, Topological aspects of complex singularities: Lefschetz theorems, topological classification, invariants
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces B. Nanayakkara, Terminal resolutions of Brauer pairs, PhD thesis, University of New Brunswick, 2010. Brauer groups of schemes, Noncommutative algebraic geometry, Global theory and resolution of singularities (algebro-geometric aspects), 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 Birational automorphisms, Cremona group and generalizations, Rational and ruled surfaces, Automorphisms of surfaces and higher-dimensional varieties, Finite automorphism groups of algebraic, geometric, or combinatorial 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 Quasivarieties and varieties of groups, Solvable groups, supersolvable groups, Model-theoretic algebra, Noncommutative algebraic geometry, Generators, relations, and presentations of groups, Automorphisms of infinite 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, Differential graded algebras and applications (associative algebraic aspects), Derived categories and associative algebras
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Automorphisms and endomorphisms, Polynomial rings and ideals; rings of integer-valued polynomials, Birational automorphisms, Cremona group and generalizations, 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 Jiang, Z.: Varieties with \(q(X)=\dim (X)\) and \(P_2(X)=2\). Ann. Sc. Norm. Super. Pisa Cl. Sci. \textbf{XI}, 243-258 (2012) Noncommutative algebraic geometry, Deformation quantization, star products, Generalizations (algebraic spaces, stacks), Noncommutative geometry (à la Connes)
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Vitória, J., Perverse coherent t-structures through torsion theories, Algebr. Represent. Theory, 17, 4, 1181-1206, (2014) Derived categories and commutative rings, Torsion theory for commutative rings, Derived categories and associative algebras, Rings arising from noncommutative algebraic geometry, 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 Park, J.; Won, J., Flexible affine cones over del Pezzo surfaces of degree 4, Eur. J. Math., 2, 304-318, (2016) Rational and ruled surfaces, Group actions on affine varieties, Affine fibrations
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces A. Treibich, Hyperelliptic \(d\)-osculating covers and rational surfaces, http://premat.fing.edu.uy/papers/2012/144.pdf. Jacobians, Prym varieties, Theta functions and curves; Schottky problem, Elliptic curves, Relationships between algebraic curves 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 Kojima, H, [supplement to ``normal del Pezzo surfaces of rank one with log canonical singularities'' by H. kojima and T. Takahashi, J. algebra \textbf{360} (2012) 53-70], J. Algebra, 377, 312-316, (2013) 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 Combinatorial aspects of finite geometries, Group actions on combinatorial structures, Rational and birational maps, Rational and ruled surfaces, Other finite nonlinear geometries
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Finite-dimensional division rings, Quadratic forms over general fields, Forms over real fields, Brauer groups (algebraic aspects), Skew fields, division rings, Algebraic functions and function fields in algebraic geometry, Rational and ruled surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Infinitesimal methods in algebraic geometry, Fundamental constructions in algebraic geometry involving higher and derived categories (homotopical algebraic geometry, derived algebraic geometry, etc.), Noncommutative algebraic geometry, Formal neighborhoods in algebraic geometry, Homotopical algebra, Quillen model categories, derivators, Derived categories of sheaves, dg categories, and related constructions 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 Applications to coding theory and cryptography of arithmetic geometry, Rational and ruled surfaces, Geometric methods (including applications of algebraic geometry) applied to coding 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, Fundamental constructions in algebraic geometry involving higher and derived categories (homotopical algebraic geometry, derived algebraic geometry, etc.), Derived categories of sheaves, dg categories, and related constructions in algebraic geometry, Derived categories and associative algebras
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Biancofiore A., Pacific Journal of Mathematics 143 pp 9-- (1990) 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 Supervarieties, Noncommutative algebraic geometry, Fine and coarse moduli spaces, Riemann surfaces; Weierstrass points; gap sequences
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Drensky, V.; Yu, J.-T., A cancellation conjecture for free associative algebras, Proc. Amer. Math. Soc., 136, 3391-3394, (2008) Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Morphisms of commutative rings, Polynomial rings and ideals; rings of integer-valued polynomials, Jacobian problem, Ordinary and skew polynomial rings and semigroup rings, Automorphisms and endomorphisms
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal 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. Salgado, D. Testa, A. Várilly-Alvarado, On the unirationality of del Pezzo surfaces of degree 2. J. Lond. Math. Soc. (2) 90(1), 121-139 (2014) Rationality questions in algebraic geometry, Varieties over finite and local fields, 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 Coverings in algebraic geometry, Coverings of curves, fundamental group, Plane and space curves, Rational and ruled surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces J. Blanc and F. Mangolte, ''Cremona groups of real surfaces'' inAutomorphisms in Birational and Affine Geometry, Springer Proc. Math. Stat.79, Springer, Cham, 2014, 35--58. Birational automorphisms, Cremona group and generalizations, 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 Kulikov, Vik. S., Plane rational quartics and K3 surfaces, Proc. Steklov Inst. Math., 294, 105-140, (2016) \(K3\) 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 Rational and ruled surfaces, Rational and birational maps
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal 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 and modules (associative rings and algebras), Quadratic and Koszul algebras, Noncommutative algebraic geometry, Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, 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 Special Riemannian manifolds (Einstein, Sasakian, etc.), Rational and ruled surfaces, Methods of global Riemannian geometry, including PDE methods; curvature restrictions, Global differential geometry of Hermitian and Kählerian 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 Vector bundles on surfaces and higher-dimensional varieties, and their moduli, Families, moduli of curves (algebraic), Rational and ruled surfaces, Algebraic moduli problems, moduli of vector bundles
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces A. Logan, The Brauer-Manin obstruction on del Pezzo surfaces of degree \( 2\) branched along a plane section of a Kummer surface, preprint, 2007. Global ground fields in algebraic geometry, Rational and ruled surfaces, Brauer groups of schemes
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces M Manetti, On some components of moduli space of surfaces of general type, Compositio Math. 92 (1994) 285 Surfaces of general type, Families, moduli, classification: algebraic theory, Rational and ruled surfaces, Differentiable mappings 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 Structure of families (Picard-Lefschetz, monodromy, etc.), Elliptic curves, Rational and ruled surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Automorphisms of surfaces and higher-dimensional varieties, \(3\)-folds, Calabi-Yau manifolds (algebro-geometric aspects), 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 Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.), Noncommutative algebraic geometry, Ordinary and skew polynomial rings and semigroup 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 T. Bauer, S. Di Rocco, B. Harbourne, M. Kapustka, A. L. Knutsen, W. Syzdek and T. Szemberg, A primer on Seshadri constants, in \textit{Interactions of Classical and Numerical Algebraic Geometry}, Contemporary Mathematics, 496, Amer. Math. Soc., Providence, RI, 2009, 33-70. Divisors, linear systems, invertible sheaves, Embeddings in algebraic geometry, Rational and ruled surfaces, 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 Schicho, J.: A degree bound for the parameterization of a rational surface. J. Pure Appl. Alg. 145, 91--105 (1999) Rational and ruled surfaces, Computational aspects of algebraic surfaces, 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 Anne-Marie Aubert, Paul Baum, and Roger Plymen, The Hecke algebra of a reductive \?-adic group: a geometric conjecture, Noncommutative geometry and number theory, Aspects Math., E37, Friedr. Vieweg, Wiesbaden, 2006, pp. 1 -- 34. Noncommutative algebraic geometry, (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.), Module categories in associative algebras, Ordinary representations and characters, 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 Rationally connected 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 DOI: 10.1017/S0027763000009041 Characteristic \(p\) methods (Frobenius endomorphism) and reduction to characteristic \(p\); tight closure, Elliptic curves, Vector bundles on curves and their moduli, Rational and ruled surfaces, Integral closure of commutative rings and ideals
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Classical problems, Schubert calculus, Rational and ruled surfaces, Syzygies, resolutions, complexes and commutative rings, 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 J. Cimprič, Y. Savchuk and K. Schmüdgen, On \(q\)-normal operators and quantum complex plane, Trans. Amer. Math. Soc. 366 (2014), 135--158. Noncommutative algebraic geometry, Real algebraic and real-analytic geometry, Rings with involution; Lie, Jordan and other nonassociative structures, Noncommutative function spaces, Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.), Algebras of unbounded operators; partial algebras of operators
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal 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, Special divisors on curves (gonality, Brill-Noether 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 S. KITAGAWA, On Mordell-Weil lattices of bielliptic fibrations on rational surfaces, J. Math. Soc. Japan, 57 (2005), pp. 137-155. Zbl1093.14051 MR2114725 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 Rational and ruled surfaces, Elliptic surfaces, elliptic or Calabi-Yau fibrations, Elementary problems in hyperbolic and elliptic geometries
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Rathmann, J.: Double structures on bordiga surfaces. Comm. algebra 17, 2363-2391 (1989) Rational and ruled surfaces, Complete intersections
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