Characteristic classes of symmetric products of complex quasi-projective varieties

Abstract

We prove generating series formulae for suitable twisted characteristic classes of symmetric products of a singular complex quasi-projective variety. More concretely, we study homology Hirzebruch classes for motivic coefficients, as well as for complexes of mixed Hodge modules. As a special case, we obtain a generating series formula for the (intersection) homology Hirzebruch classes of symmetric products. In some cases, the latter yields a similar formula for twisted homology L-classes generalizing results of Hirzebruch–Zagier and Moonen. Our methods also apply to the study of Todd classes of (complexes of) coherent sheaves, as well as Chern classes of (complexes of) constructible sheaves, generalizing to arbitrary coefficients results of Moonen and respectively Ohmoto.

Document Details

Document Type
Pub Defense Publication
Publication Date
Jan 21, 2015
Source ID
10.1515/crelle-2014-0114

Entities

People

  • Julius L. Shaneson
  • Jörg Schürmann
  • Laurentiu Maxim
  • Shoji Yokura
  • Sylvain E. Cappell

Organizations

  • Kagoshima University
  • New York University
  • University of Münster
  • University of Pennsylvania
  • University of Wisconsin–Madison

Tags

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Linear Algebra