Geometry & Topology

Equivariant characteristic classes of external and symmetric products of varieties

Laurenţiu Maxim and Jörg Schürmann

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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

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

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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