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4 results on '"14 Algebraic geometry::14B Local theory [Classificació AMS]"'

1. Localizations at hyperplane arrangements: combinatorics and D-modules

Author

Álvarez Montaner, Josep, Jiménez, Francisco Jesús Castro, Enríquez, José María Ucha, Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I, and Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions

Subjects
Geometry, Algebraic, Hyperplane arrangements, Characteristic cycle, Àlgebra diferencial, Localization, 14 Algebraic geometry::14B Local theory [Classificació AMS], Espais analítics, 32 Several complex variables and analytic spaces::32C Analytic spaces [Classificació AMS], Geometria algèbrica, Analytic spaces, Logarithmic D-modules, Differential algebra, 13 Commutative rings and algebras::13N Differential algebra [Classificació AMS]
Abstract

We describe an algorithm deciding if the annihilating ideal of the meromorphic function 1 f , where f = 0 defines an arrangement of hyperplanes, is generated by linear differential operators of order 1. The algorithm is based on the comparison of two characteristic cycles and uses a combinatorial description due to `Alvarez-Montaner, Garc´ıa–L´opez and Zarzuela of the characteristic cycle of the D-module of meromorphic functions with respect to f.

Published
2004

2. Versal deformations in generalized flag manifolds

Author

X. Puerta, Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I, and Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions

Subjects
Pure mathematics, 14 Algebraic geometry::14M Special varieties [Classificació AMS], 14 Algebraic geometry::14B Local theory [Classificació AMS], 93C Control systems, guided systems [Control], Generalized flag manifold, Sistemes de control, Grassmannian, 93 Systems Theory, Control::93C Control systems, guided systems [Classificació AMS], Discrete Mathematics and Combinatorics, Equivalence relation, Geometria algèbrica, Sistemes, Teoria de, System theory, generalized flag manifold, Control::93B Controllability, observability, and system structure [Classificació AMS], Mathematics::Representation Theory, Mathematics, orbit space, Grassmann manifold, Numerical Analysis, 93 Systems Theory [Classificació AMS], Versal deformation, Algebra and Number Theory, Group (mathematics), Orbit space, Mathematical analysis, Varietats (Matemàtica), Action (physics), Manifold, 93B Controllability, observability, and system structure [Control], Geometry, Algebraic, Geometry and Topology, Flag (geometry)
Abstract

We find explicit miniversal deformations of flags in the generalized flag manifolds, with regard a natural equivalence relation defined by the group action that keeps fixed the reference flag.

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3. A Koszul complex over skew polynomial rings

Author

Santiago Zarzuela, Josep Àlvarez Montaner, Alberto F. Boix, Universitat Politècnica de Catalunya. Departament de Matemàtiques, and Universitat Politècnica de Catalunya. GEOMVAP - Geometria de Varietats i Aplicacions

Subjects
Pure mathematics, 16 Associative rings and algebras::16S Rings and algebras arising under various constructions [Classificació AMS], Endomorphism, Rings (Algebra), Polynomial ring, Frobenius algebras, Commutative rings, 14 Algebraic geometry::14B Local theory [Classificació AMS], Cartier algebras, Koszul complex, 010103 numerical & computational mathematics, Anells commutatius, 01 natural sciences, Mathematics::Algebraic Topology, Àlgebra commutativa, Mathematics::K-Theory and Homology, 13 Commutative rings and algebras::13A General commutative ring theory [Classificació AMS], 0101 mathematics, Morfismes (Matemàtica), Morphisms (Mathematics), Mathematics, Algebra and Number Theory, Ideal (set theory), Mathematics::Commutative Algebra, 010102 general mathematics, Mathematics::Rings and Algebras, Skew, Matemàtiques i estadística [Àrees temàtiques de la UPC], Geometry, Algebraic, Skew polynomial rings, Anells (Àlgebra), 13 Commutative rings and algebras::13B Ring extensions and related topics [Classificació AMS], Geometria algebraica, Commutative algebra, Resolution (algebra)
Abstract

We construct a Koszul complex in the category of left skew polynomial rings associated with a flat endomorphism that provides a finite free resolution of an ideal generated by a Koszul regular sequence

4. Local cohomology, arrangement of subspaces and monomial ideals

Author

Álvarez Montaner, Josep|||0000-0001-6793-368X, García López, Ricardo, Zarzuela Armengou, Santiago, Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I, and Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions

Subjects
Geometry, Algebraic, Subspaces, 14 Algebraic geometry::14B Local theory [Classificació AMS], Monomial Ideals, Homologia, Teoria d', Geometria algèbrica, 13 Commutative rings and algebras::13D Homological methods [Classificació AMS], Cohomology, Algebra, Homological

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