Algebraic computation of some intersection D-modules

Abstract

Let D ⊂ ℂ n be a locally quasi-homogeneous free divisor (e.g. a free hyperplane arrangement), ε an integrable logarithmic connection with respect to D and ℒthe local system of horizontal sections of ε on X - D. Let IC X (ε) be the holonomic regular D X -module whose de Rham complex is the intersection complex IC X (ℒ) of Deligne-Goresky-MacPherson. In this paper we show how to use our previous results on the algebraic description of IC X (ε) in order to obtain explicit presentations of it. Concrete examples for n = 2 are included. © Springer-Verlag Berlin Heidelberg 2006.