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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal 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. Kassel and C. Reutenauer, Complete determination of the zeta function of the Hilbert scheme of n points on a two-dimensional torus, \textit{Ramanujan J.}, to appear. Noncommutative algebraic geometry, Exact enumeration problems, generating functions, Algebraic theory of languages and automata, Combinatorics on words, Algebraic functions and function fields in algebraic geometry, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Katzarkov, L., Lupercio, E., Meersseman, L., Verjovsky, A.: The definition of a non-commutative toric variety. In: Tillmann, U., Galatius, S., Sinha, D. (eds.) Algebraic Topology: Applications and New Directions. Contemporary Mathematics, vol. 620. AMS pp. 223-250 (2014) Noncommutative algebraic geometry, Toric varieties, Newton polyhedra, Okounkov bodies, Algebraic moduli of abelian varieties, classification, Combinatorics and topology in relation with holomorphic dynamical systems
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal 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, Deformations of singularities, Local deformation theory, Artin approximation, etc., Formal methods and deformations in algebraic geometry
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Déserti, J; Grivaux, J, Automorphisms of rational surfaces with positive entropy, Indiana Univ. Math. J., 60, 1589-1622, (2011) Birational automorphisms, Cremona group and generalizations, Topological entropy, Complex spaces with a group of automorphisms, Rational and ruled surfaces, Automorphisms of surfaces and higher-dimensional varieties, Dynamical systems over complex numbers
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal 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 \(K\)-theory, Proceedings, conferences, collections, etc. pertaining to global analysis, 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 Combinatorial aspects of finite geometries, Exact enumeration problems, generating functions, 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 Fibrations, degenerations in algebraic geometry, Rational and ruled surfaces, Vector bundles on surfaces and higher-dimensional varieties, and their moduli, Rationality questions in algebraic geometry, Rational and unirational varieties, Rational and birational maps, Special surfaces, Quadratic spaces; Clifford algebras
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative algebraic geometry, Formal methods and deformations in algebraic geometry
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Fujisawa T.: On non-rational numerical del Pezzo surfaces. Osaka J. Math. 32, 613--636 (1995) 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 Burban, Igor; Drozd, Yuriy; Gavran, Volodymyr: Singular curves and quasi-hereditary algebras. (2015) Noncommutative algebraic geometry, Global theory and resolution of singularities (algebro-geometric aspects)
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative algebraic geometry, Theta functions and abelian varieties, Supersymmetry and quantum mechanics, Nilpotent and solvable Lie groups, Unitary representations of locally compact 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 Number-theoretic analogues of methods in Nevanlinna theory (work of Vojta et al.), Value distribution theory in higher dimensions, Global ground fields in algebraic geometry, Farey sequences; the sequences \(1^k, 2^k, \dots\), Schmidt Subspace Theorem and applications, Arithmetic varieties and schemes; Arakelov theory; heights, Rational and ruled surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Lieven Le Bruyn, Simultaneous equivalence of square matrices, Séminaire d'Algèbre Paul Dubreil et Marie-Paul Malliavin, 39ème Année (Paris, 1987/1988) Lecture Notes in Math., vol. 1404, Springer, Berlin, 1989, pp. 127 -- 136. Rational and unirational varieties, Endomorphism rings; matrix rings, Brauer groups of schemes, Vector bundles on surfaces and higher-dimensional varieties, and their moduli, Canonical forms, reductions, classification, General theory of PDEs and systems of PDEs with constant coefficients
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal 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, Gröbner basis, Mordell-Weil lattices and deformation of singularities. I, Proc. Japan Acad. Ser. A Math. Sci. 86 (2010), no. 1, 21-26. Rational and ruled surfaces, Elliptic surfaces, elliptic or Calabi-Yau fibrations, Elliptic curves over global fields
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Brian Harbourne, ``Anticanonical rational surfaces'', Trans. Am. Math. Soc.349 (1997) no. 3, p. 191-1208 Divisors, linear systems, invertible sheaves, Rational and ruled surfaces, Rational and unirational varieties, 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 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 Marcolli, Matilde; Tabuada, Gonçalo, Noncommutative numerical motives, Tannakian structures, and motivic Galois groups, J. Eur. Math. Soc. (JEMS), 18, 3, 623-655, (2016) Noncommutative algebraic geometry, (Equivariant) Chow groups and rings; motives, (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, 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 Li, Y.-C.; Yu, J.-T., Degree estimate for subalgebras, J. Algebra, 362, 92-98, (2012) Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Polynomial rings and ideals; rings of integer-valued polynomials, Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Automorphisms and endomorphisms, Computational aspects of associative rings (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 Noncommutative algebraic geometry, Derived categories of sheaves, dg categories, and related constructions in algebraic geometry, Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (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 van Oystaeyen, F.: Virtual Topology and Functor Geometry. Lecture Notes in Pure and Applied Mathematics, vol. 256. Chapman and Hall, New York (2007) Research exposition (monographs, survey articles) pertaining to category theory, Categories in geometry and topology, Noncommutative algebraic geometry
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces A. Bayer and Yu. Manin, ''(Semi)simple Exercises in Quantum Cohomology,'' in Proc. Fano Conf., Torino, Italy, 2002 (Univ. Torino, Torino, 2004), pp. 143--173; arXiv:math/0103164. Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), Fano varieties, Rational and ruled surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Failla, G., Lahyane, M., Molica Bisci, G.: On the finite generation of the monoid of effective divisor classes on rational surfaces of type (\textit{n}, \textit{m}). Atti Accademia Peloritana Pericolanti Cl. Sci. Fis., Mat. Natur. LXXXIV (2006). https://doi.org/10.1478/C1A0601001 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 Fioresi R., Lledo M.A., Varadarajan V.S.: On the deformation quantization of affine algebraic varieties. Int. J. Math. 16, 419--436 (2005) arXiv:math/0406196v1 [math.QA] Deformation quantization, star products, 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 Lahyane, Mustapha; Harbourne, Brian, Irreducibility of \(-1\)-classes on anticanonical rational surfaces and finite generation of the effective monoid, Pacific J. Math., 218, 1, 101-114, (2005) 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 Kanel-Belov, A.; Elishev, A., On planar algebraic curves and holonomic \(\mathcal{D}\)-modules in positive characteristic, J. Algebra Appl., 15, 8, 1650155, (2016) Noncommutative algebraic geometry, Automorphisms and endomorphisms, Rings of differential operators (associative algebraic 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 [Ru1] D. Rumynin,Hopf-Galois extensions with central invariants and their geometric properties, Alg. Rep. Th.,1 (1998), 353--381. 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 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 Bartocci, C; Macrí, E, Classification of Poisson surfaces, Commun. Contemp. Math., 7, 89-95, (2005) Rational and ruled surfaces, Poisson manifolds; Poisson groupoids and algebroids
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Schicho, J., The parametric degree of a rational surface, Math. Z., 254, 185-198, (2006) 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 Module categories in associative algebras, Representations of quivers and partially ordered sets, Rings arising from noncommutative algebraic geometry, Derived categories of sheaves, dg categories, and related constructions in algebraic geometry, Derived categories, triangulated categories
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Hasse principle, weak and strong approximation, Brauer-Manin obstruction, \(K3\) surfaces and Enriques surfaces, Rational and ruled surfaces, Brauer groups of schemes, Rational points
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal 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. H. Lenagan and L. Rigal, Quantum analogues of Schubert varieties in the Grassmannian, Glasg. Math. J. 50 (2008), no. 1, 55 -- 70. Grassmannians, Schubert varieties, flag manifolds, Divisibility, noncommutative UFDs, Rings arising from noncommutative algebraic geometry, Noetherian rings and modules (associative rings and algebras)
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Toric varieties, Newton polyhedra, Okounkov bodies, Families, moduli, classification: algebraic theory, Rational and ruled surfaces, Foliations (differential geometric aspects), Foliations in differential topology; geometric 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, 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 Abelian categories, Grothendieck categories, Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.), Noncommutative algebraic geometry, Singularities of surfaces or higher-dimensional varieties, Relative homological algebra, projective classes (category-theoretic aspects)
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces N. Joglar-Prieto, Rational surfaces and regular maps into the 2-dimensional sphere, Math. Z. 234 (2000), 399-405. Zbl0968.14033 MR1765888 Topology of real algebraic varieties, Rational and ruled surfaces, Abstract approximation theory (approximation in normed linear spaces and other abstract 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 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 Supermanifolds and graded manifolds, Analysis on supermanifolds or graded manifolds, Noncommutative algebraic geometry, Group actions on varieties or schemes (quotients), Formal power series rings, Noncommutative local and semilocal rings, perfect rings, Superalgebras
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal 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. Plotkin, Ukr. Math. J. 54(6), 1019 (2002). Varieties and morphisms, Varieties, Noncommutative algebraic geometry, Local categories and functors
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal 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, Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.), McKay correspondence, Representations of quivers and partially ordered sets, Cohen-Macaulay modules, Group rings of finite groups and their modules (group-theoretic aspects), Singularities in algebraic geometry, Ordinary representations and characters
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal 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 surfaces, Rational and ruled surfaces, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Keeler, D. S.: The rings of noncommutative projective geometry. Advances in algebra and geometry, 195-207 (2003) Noncommutative algebraic geometry, Projective techniques in algebraic geometry, Noetherian rings and modules (associative rings and algebras)
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces \(n\)-folds (\(n>4\)), Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.), Linkage, complete intersections and determinantal ideals, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Rational and ruled surfaces, \(K3\) surfaces and Enriques surfaces, Calabi-Yau manifolds (algebro-geometric aspects), Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties, Rational and unirational varieties, 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 Helton, J. W.; Klep, I.; McCullough, S., Free convex algebraic geometry, Semidefinite Optimization and Convex Algebraic Geometry, 341-405, (2013), SIAM Noncommutative algebraic geometry, Real algebraic sets, Semialgebraic sets and related spaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Twistor theory, double fibrations (complex-analytic aspects), Grassmannians, Schubert varieties, flag manifolds, Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory), Rational and ruled surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces DOI: 10.1006/jabr.1993.1054 Noncommutative topology, Noncommutative differential 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 Müller-Hoissen, Folkert, Introduction to noncommutative geometry of commutative algebras and applications in physics, (Garcia, A.; Lämmerzahl, C.; Macias, A.; Matos, T.; Nuñez, D., Recent developments in gravitation and mathematical physics, Proceedings of the second Mexican school on gravitation and mathematical physics, (1997), Science Network Publishing) Noncommutative topology, Noncommutative differential geometry, Classical field theories, Noncommutative algebraic geometry, Classical or axiomatic geometry 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 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 13. Giraldo, L., Sols, I.: The irregularity of ruled surfaces in \(\mathbb{P}^3\) . Dedicated to the memory of Fernando Serrano, Collect Math., 49 (1998), no. 2--3, 325--334 Rational and ruled surfaces, Plane and space curves, \(4\)-folds
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Compactification of analytic spaces, Compact complex 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 \(3\)-folds, Rational and ruled surfaces, Vector bundles on surfaces and higher-dimensional varieties, and their moduli, Parametrization (Chow and Hilbert schemes), Algebraic moduli problems, moduli of vector bundles, Varieties of low degree, Adjunction problems
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative algebraic geometry, Projective techniques in algebraic geometry, Quadratic and Koszul algebras, \(K\)-theory and homology; cyclic homology and cohomology, \(K\)-theory 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 D. Bourqui, La conjecture de Manin géométrique pour une famille de quadriques intrinsèques , Manuscripta Math. 135 (2011), no. 4, 1-41. Global ground fields in algebraic geometry, Heights, Positive characteristic ground fields in algebraic geometry, Rational and ruled surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Algebraic structures, Noncommutative algebraic geometry, 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 V. A. Iskovskikh, On finite subgroups of the Cremona group, Vietnam J. Math. 33 (2005), Special Issue, 61--80. Birational automorphisms, Cremona group and generalizations, Rational and ruled surfaces, Automorphisms of surfaces and higher-dimensional varieties
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces DOI: 10.2996/kmj/1104247353 \(3\)-folds, Rational and ruled surfaces, Divisors, linear systems, invertible sheaves, Adjunction problems
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Ryoichi Kobayashi and Andrey N. Todorov, Polarized period map for generalized \?3 surfaces and the moduli of Einstein metrics, Tohoku Math. J. (2) 39 (1987), no. 3, 341 -- 363. Moduli, classification: analytic theory; relations with modular forms, Compact complex surfaces, Special Riemannian manifolds (Einstein, Sasakian, etc.), Homogeneous spaces and generalizations, Global differential geometry of Hermitian and Kählerian manifolds, Complex-analytic moduli problems, 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 Z. Sela, ''Diophantine Geometry over Groups. V2: Quantifier Elimination. II,'' Geom. Funct. Anal. 16(3), 537--706 (2006). 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 A. Auel, M. Bernardara and M. Bolognesi, Fibrations in complete intersections of quadrics, Clifford algebras, derived categories, and rationality problems, J. Math. Pures Appl. (9) 102 (2014), 249-291. Rationality questions in algebraic geometry, Quadratic forms over local rings and fields, General ternary and quaternary quadratic forms; forms of more than two variables, Quadratic spaces; Clifford algebras, Brauer groups of schemes, Rational and ruled surfaces, Homogeneous spaces and generalizations, 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 Yang-Mills and other gauge theories in quantum field theory, Yang-Mills and other gauge theories in mechanics of particles and systems, Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory), Differential algebra, Noncommutative algebraic geometry, Geometric theory, characteristics, transformations in context of PDEs
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Orlov, D. O.: Quasicoherent sheaves in commutative and noncommutative geometry. Izv. ross. Akad. nauk ser. Mat. 67, No. 3, 119-138 (2003) Noncommutative algebraic geometry, Grothendieck topologies and Grothendieck topoi
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Valuations and their generalizations for commutative rings, 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 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 Ciliberto, C; Flamini, F, Extensions of line bundles and brill-Noether loci of rank-two vector bundles on a general curve, Rev. Roum. Math. Pures Appl., 60, 201-255, (2015) Vector bundles on curves and their moduli, Algebraic moduli problems, moduli of vector bundles, Rational and ruled surfaces, Determinantal varieties, 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 A. Biancofiore andG. Ceresa, Remarks onk-spannedness for Algebraic Surfaces. Rend. Sem. Mat. Univers. Politecn. Torino46 (1988), 343--352. 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 Palka, K., Recent progress in the geometry of \(\mathbb{Q}\)-acyclic surfaces, (Affine Algebraic Geometry: The Russell Festschrift, CRM Proc. Lecture Notes, vol. 54, (2011), Amer. Math. Soc. Providence, RI), 271-287 Classification of affine varieties, Singularities of 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 Brüstle, T.; Hille, L.: Matrices over upper triangular bimodules and \({\Delta}\)-filtered modules over quasi-hereditary algebras. Coll. math. 83, 295-303 (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, Vector bundles on surfaces and higher-dimensional varieties, and their moduli, Special 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 Configurations and arrangements of linear subspaces, 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 Fukasawa, S.: Developable varieties in positive characteristic. Hiroshima Math. J. 35, 167--182 (2005) Projective techniques in algebraic geometry, Rational and ruled surfaces, Arithmetic ground fields for surfaces or higher-dimensional varieties
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Rational and ruled surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Takahashi, Certain relative quadric hypersurfaces of 3-dimensional projective space bundles over a projective curve, Geom. Dedicata 154 pp 183-- (2011) \(3\)-folds, Rational and ruled surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Yu, F, Note on families of semistable curves over \({\mathbb{P}}^1\) with 4 singular fibers whose Jacobian are non-compact, Sci. China, 53, 1711-1714, (2010) Families, moduli, classification: algebraic theory, Rational and ruled surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Friedman R., Qin Z., On complex surfaces diffeomorphic to rational surfaces, Invent. Math., 1995, 120(1), 81--117 Surfaces of general type, 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 Shustin, E.: On higher genus Welschinger invariants of del Pezzo surfaces. \textit{IMRN} 2015, 6907--6940. DOI: 10.1093/imrn/rnu148. Rational and ruled surfaces, Real algebraic sets, Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (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 Gimigliano, Stable postulation and stable ideal generation: conjectures for fat points in the plane, Bull. Belg. Math. Soc. Simon Stevin 16 (5) pp 853-- (2009) Divisors, linear systems, invertible sheaves, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), 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 Altavilla, A., Twistor interpretation of slice regular functions, J. Geom. Phys., 123, 184-208, (2018) Twistor methods in differential geometry, Functions of hypercomplex variables and generalized variables, Global differential geometry of Hermitian and Kählerian manifolds, 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, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Residual properties and generalizations; residually finite groups, Model-theoretic algebra, Word problems, other decision problems, connections with logic and automata (group-theoretic aspects), Applications of logic to group theory, Noncommutative algebraic geometry
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Xavier Gómez-Mont, Holomorphic foliations in ruled surfaces, Trans. Amer. Math. Soc. 312 (1989), no. 1, 179 -- 201. Foliations in differential topology; geometric theory, Rational and ruled surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Black holes, Singular and oscillatory integrals (Calderón-Zygmund, etc.), Applications of differential geometry to physics, Nonlinear oscillations and coupled oscillators for ordinary differential equations, Noncommutative algebraic geometry
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces DOI: 10.1007/s00208-007-0157-4 Rational and ruled 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 Billard, H, Répartition des points rationnels des surfaces géométriquement réglées rationnelles, Astérisque, 251, 79-89, (1998) Varieties over global fields, Rational points, Global ground fields in algebraic geometry, Rational and ruled surfaces
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces ---, Sur le sous-groupe de décomposition d'une courbe irrationnelle dans le groupe de Cremona du plan, Michigan Math. J. 55 (2007), 285-298. Birational automorphisms, Cremona group and generalizations, Rational and birational maps, 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 Rational and unirational varieties, Group actions on varieties or schemes (quotients), 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 Chi W.C., Bull.Austral.Math.Soc 50 pp 245-- (1994) Galois cohomology, Galois cohomology, Finite-dimensional division rings, Endomorphism rings; matrix rings, 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 Rational and ruled surfaces, Projective techniques 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 Ardizzoni A, Brzeziński T, Menini C. Formally smooth bimodules. J Pure Appl Algebra, 2008, 212: 1072--1085 Bimodules in associative algebras, Noncommutative algebraic geometry, (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.), Relative homological algebra, projective classes (category-theoretic aspects)
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces M. Artebani, A. Garbagnati, A. Laface: Cox rings of extremal rational elliptic surfaces. To appear in Transactions of the AMS. Preprint, arXiv:1302.4361. 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 H. Kojima, Notes on minimal normal compactifications of \(\mathbb{C}\)2/G.Nihonkai Math. J. 54 (2004), 127--136. Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Group actions on affine varieties, Singularities of surfaces or higher-dimensional varieties, Group actions on varieties or schemes (quotients), 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 Flenner, H., Kaliman, S., Zaidenberg, M.: Corrigendum to our paper ``Birational transformations of weighted graphs''. Affine Algebraic Geometry, CRM Proceedings of the Lecture Notes, vol. 54, pp. 35-38. American Mathematical Society, Providence (2011) 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 Collections of abstracts of lectures, Proceedings, conferences, collections, etc. pertaining to algebraic geometry, Proceedings, conferences, collections, etc. pertaining to associative rings and algebras, Proceedings, conferences, collections, etc. pertaining to nonassociative 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 Computational aspects of algebraic curves, Rational and ruled surfaces, Finite ground fields in algebraic geometry, Rational and birational maps, 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 Divisors, linear systems, invertible sheaves, Rational and ruled surfaces, Bundle convexity, Convex sets in \(2\) dimensions (including convex curves), Syzygies, resolutions, complexes 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 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 P. Salberger, On the arithmetic of conic bundle surfaces , Séminaire de Théorie des Nombres, Paris 1985-86, Progr. Math., vol. 71, Birkhäuser Boston, Boston, MA, 1987, pp. 175-197. Rational and ruled surfaces, Algebraic cycles, Arithmetic ground fields for surfaces or higher-dimensional varieties, Rational and unirational varieties, Arithmetic problems in algebraic geometry; Diophantine 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 Holay, S. H.: Free resolutions of the defining ideal of certain rational surfaces. Manuscripta math. 90, No. 1, 23-37 (1996) Rational and ruled surfaces, Syzygies, resolutions, complexes 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 Yu. A. Drozd and D. E. Voloshyn, ''Vector bundles over noncommutative nodal curves,'' Ukr. Mat. Zh., 64, No. 2, 185--199 (2012); English translation: Ukr. Math. J., 64, No. 2, 208--224 (2012). Noncommutative algebraic geometry, Vector bundles on curves and their moduli
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Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces 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 M. Beltrametti, E. Carletti, D. Gallarati, G. Bragadin, Lectures on Curves Surfaces and Projective varieties: A classical view of algebraic geometry, Translated from the Italian by Francis Sullivan, European Mathematical Society (EMS), Zürich, 2009. Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Rational and birational maps, Curves in algebraic geometry, Birational geometry, Rational and ruled surfaces
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