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

2015/09/06 by Oaku, Toshinori
#13D45 #14F10 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1509.01813

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 ∈ R defines a hyperplane arrangement in the affine space Kⁿ. Then the length and the multiplicity of the 1st local cohomology group H¹_(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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