Geometry & Topology

Equivariant characteristic classes of external and symmetric products of varieties

Laurenţiu Maxim and Jörg Schürmann

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Abstract

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.

Article information

Source
Geom. Topol., Volume 22, Number 1 (2018), 471-515.

Dates
Received: 23 February 2016
Revised: 22 March 2017
Accepted: 2 May 2017
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513774917

Digital Object Identifier
doi:10.2140/gt.2018.22.471

Mathematical Reviews number (MathSciNet)
MR3720348

Zentralblatt MATH identifier
06805083

Subjects
Primary: 55S15: Symmetric products, cyclic products 57R20: Characteristic classes and numbers
Secondary: 20C30: Representations of finite symmetric groups

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

Citation

Maxim, Laurenţiu; Schürmann, Jörg. Equivariant characteristic classes of external and symmetric products of varieties. Geom. Topol. 22 (2018), no. 1, 471--515. doi:10.2140/gt.2018.22.471. https://projecteuclid.org/euclid.gt/1513774917


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