Localizations at hyperplane arrangements: combinatorics and D-modules

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Title:	Localizations at hyperplane arrangements: combinatorics and D-modules
Author:	Álvarez Montaner, Josep; Jiménez, Francisco Jesús Castro; Enríquez, José María Ucha
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
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.
Subject(s):	-Analytic spaces -Geometry, Algebraic -Differential algebra -Characteristic cycle -Localization -Hyperplane arrangements -Logarithmic D-modules -Espais analítics -Geometria algèbrica -Àlgebra diferencial -Classificació AMS::14 Algebraic geometry::14B Local theory -Classificació AMS::13 Commutative rings and algebras::13N Differential algebra -Classificació AMS::32 Several complex variables and analytic spaces::32C Analytic spaces
Rights:	Attribution-NonCommercial-NoDerivs 2.5 Spain http://creativecommons.org/licenses/by-nc-nd/2.5/es/
Document type:	Article
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