The Hilbert series of Hodge ideals of hyperplane arrangements

Bradley Dirks and Mircea Mustaţă

Journal of Singularities
volume 20 (2020), 232-250

Received: 10 April 2020. Received in revised form: 7 July 2020

DOI: 10.5427/jsing.2020.20j

Add a reference to this article to your citeulike library.


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 Poincaré polynomial of the arrangement.


2010 Mathematical Subject Classification:

14F10, 14B05, 32S22


Author(s) information:

Bradley Dirks Mircea Mustaţă
Department of Mathematics Department of Mathematics
University of Michigan University of Michigan
530 Church Street 530 Church Street
Ann Arbor, MI 48109, USA Ann Arbor, MI 48109, USA
email: bdirks@umich.edu email: mmustata@umich.edu