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