Volume 22, issue 1 (2018)

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Equivariant characteristic classes of external and symmetric products of varieties

Laurenţiu Maxim and Jörg Schürmann

Geometry & Topology 22 (2018) 471–515

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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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
Received: 23 February 2016
Revised: 22 March 2017
Accepted: 2 May 2017
Published: 31 October 2017
Proposed: Jim Bryan
Seconded: Dan Abramovich, Ralph Cohen
Laurenţiu Maxim
Department of Mathematics
University of Wisconsin-Madison
Madison, WI
United States
Jörg Schürmann
Mathematische Institut
Universität Münster