The Hilbert series of Hodge ideals of hyperplane arrangements

2020/03/26 by Bradley Dirks, Dirks, Bradley, Mircea Mustata +1
Mathematics · #14B05 #14F10 #32S22 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14B05 #msc:14F10 #msc:32S22

paper · pdf · doi:10.48550/arxiv.2003.11681

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

arxiv created 2020/07/07 · arxiv updated 2020/07/08

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.

Related

• Power structure over the Grothendieck ring of varieties and generating series of Hilbert schemes of points
• Hodge ideals and minimal exponents of ideals
• Hodge spectrum of hyperplane arrangements
• An algorithm for Hodge ideals
• Generating series of classes of Hilbert schemes of points on orbifolds