The Hilbert series of Hodge ideals of hyperplane arrangements

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.

19 pages; v.2: details added regarding the equivariant motivic Chern class, following suggestions of J. Schuermann; v.3: reference added to a result of Xia Liao, final version, to appear in Journal of Singularities