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arXiv · 2003.11681

The Hilbert series of Hodge ideals of hyperplane arrangements

Bradley Dirks·Mircea Mustata
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Abstract

Given a reduced effective divisor D on a smooth variety X, we describe the generating function for the classes of the Hodge ideals of D in the Grothendieck group of coherent sheaves on X in terms of the motivic Chern class of the complement of the support of D. As an application, we compute the generating function for the Hilbert series of Hodge ideals of a hyperplane arrangement in terms of the Poincare polynomial of the arrangement.

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Bradley Dirks, Mircea Mustata. 2020-03-26. The Hilbert series of Hodge ideals of hyperplane arrangements. https://arxiv.org/abs/2003.11681

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