Equivariant characteristic classes of external and symmetric products of varieties

We obtain refined generating series formulae for equivariant characteristic classes of external and symmetric products of singular complex quasiprojective varieties. More concretely, we study equivariant versions of Todd, Chern and Hirzebruch classes for singular spaces, with values in delocalized Borel–Moore homology of external and symmetric products. As a byproduct, we recover our previous characteristic class formulae for symmetric products and obtain new equivariant generalizations of these results, in particular also in the context of twisting by representations of the symmetric group.

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Keywords

characteristic classes, orbifold classes, Hirzebruch– and Lefschetz–Riemann–Roch, external and symmetric products of varieties, generating series, representations of symmetric groups

Mathematical Subject Classification 2010

Primary: 55S15, 57R20

Secondary: 20C30

References

Publication

Received: 23 February 2016

Revised: 22 March 2017

Accepted: 2 May 2017

Published: 31 October 2017

Proposed: Jim Bryan

Seconded: Dan Abramovich, Ralph Cohen

Authors

Laurenţiu Maxim
Department of Mathematics University of Wisconsin-Madison Madison, WI United States
http://www.math.wisc.edu/~maxim/
Jörg Schürmann
Mathematische Institut Universität Münster Münster Germany
http://wwwmath.uni-muenster.de/u/jschuerm

Volume 22, issue 1 (2018)

Laurenţiu Maxim and Jörg Schürmann

Abstract