Characteristic classes of symmetric products of complex quasi-projective varieties

Characteristic classes of symmetric products of complex quasi-projective varieties

We prove generating series formulae for suitable twisted characteristic classes of symmetric products of a complex quasi-projective variety. More concretely, we study homology Hirzebruch classes for motivic coefficients, as well as for complexes of mixed Hodge modules. As a special case, we obtain a...

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Veröffentlicht in:Journal für die reine und angewandte Mathematik 2017-07, Vol.2017 (728), p.35-63
Hauptverfasser: Cappell, Sylvain E., Maxim, Laurentiu, Schürmann, Jörg, Shaneson, Julius L., Yokura, Shoji
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container_issue 728
container_start_page 35
container_title Journal für die reine und angewandte Mathematik
container_volume 2017
creator Cappell, Sylvain E.
Maxim, Laurentiu
Schürmann, Jörg
Shaneson, Julius L.
Yokura, Shoji
description We prove generating series formulae for suitable twisted characteristic classes of symmetric products of a complex quasi-projective variety. More concretely, we study homology Hirzebruch classes for motivic coefficients, as well as for complexes of mixed Hodge modules. As a special case, we obtain a generating series formula for the (intersection) homology Hirzebruch classes of symmetric products. In some cases, the latter yields a similar formula for twisted homology -classes generalizing results of Hirzebruch–Zagier and Moonen. Our methods also apply to the study of Todd classes of (complexes of) coherent sheaves, as well as Chern classes of (complexes of) constructible sheaves, generalizing to arbitrary coefficients results of Moonen and respectively Ohmoto.
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