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OPERATIONS WITH REGULAR HOLONOMIC DMODULES WITH SUPPORT A NORMAL CROSSING
 

Summary: OPERATIONS WITH REGULAR HOLONOMIC D­MODULES
WITH SUPPORT A NORMAL CROSSING
JOSEP ‘
ALVAREZ MONTANER
Abstract. The aim of this work is to describe some operations in the category
of regular holonomic D­modules with support a normal crossing and variation
zero introduced in [2]. These operations will allow us to compute the Bass
numbers and the dual Bass numbers of these modules.
1. Introduction
Let X = C n , OX the sheaf of holomorphic functions in C n , and DX the sheaf
of di#erential operators in C n with holomorphic coe#cients. Galligo, Granger and
Maisonobe [8], described in terms of linear algebra the category Mod(DX ) T
hr of
regular holonomic DX ­modules such that their solution complex RHomDX (M,OX )
are perverse sheaves relatively to the stratification given by the union T of the
coordinate hyperplanes in C n .
In Section 2 we recall the definition and the basic properties of the category
D T
v=0 of modules with variation zero introduced in [2] (see also [3]). Moreover, we
define the category of modules with unipotent monodromy that is also a full abelian

  

Source: Alvarez Montaner, Josep - Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya

 

Collections: Mathematics