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2 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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