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