Length and multiplicity of the local cohomology with support in a hyperplane arrangement

Abstract

Let $R$ be the polynomial ring in $n$ variables with coefficients in a field $K$ of characteristic zero. Let $D_n$ be the $n$-th Weyl algebra over $K$. Suppose that $f\in R$ defines a hyperplane arrangement in the affine space $K^n$. Then the length and the multiplicity of the 1st local cohomology group $H_{(f)}^1(R)$ as left $D_n$-module coincide and are explicitly expressed in terms of the Poincaré polynomial or the Möbius function of the arrangement.

8 pages

Cited by in corpus (1)

• Length of Perverse Sheaves on Hyperplane Arrangements