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

Toshinori Oaku

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arXiv · 1509.01813

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

Toshinori Oaku

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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 $H^1_{(f)}(R)$ as left $D_n$-module coincide and are explicitly expressed in terms of the Poincaré polynomial or the Möbius function of the arrangement.

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Toshinori Oaku. 2015-09-06. Length and multiplicity of the local cohomology with support in a hyperplane arrangement. https://arxiv.org/abs/1509.01813

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