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Journal für die reine und angewandte Mathematik

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Volume 2017, Issue 728


Characteristic classes of symmetric products of complex quasi-projective varieties

Sylvain E. Cappell / Laurentiu Maxim / Jörg Schürmann / Julius L. Shaneson / Shoji Yokura
  • Department of Mathematics and Computer Science, Faculty of Science, Kagoshima University, 21-35 Korimoto 1-chome, Kagoshima 890-0065, Japan
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Published Online: 2015-01-21 | DOI: https://doi.org/10.1515/crelle-2014-0114


We prove generating series formulae for suitable twisted characteristic classes of symmetric products of a singular 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 L-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.

To the memory of Friedrich Hirzebruch


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About the article

Received: 2012-08-03

Published Online: 2015-01-21

Published in Print: 2017-07-01

S. Cappell and J. Shaneson are partially supported by DARPA-25-74200-F6188. L. Maxim was partially supported by grants from NSF (1005338 and 1304999), NSA (H98230-14-1-0130), by a grant of the Ministry of National Education (CNCS-UEFISCDI project number PN-II-ID-PCE-2012-4-0156), and by a research fellowship from the Max-Planck-Institut für Mathematik, Bonn. J. Schürmann is supported by the SFB 878 “groups, geometry and actions”. S. Yokura is partially supported by Grant-in-Aid for Scientific Research (No. 24540085), the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2017, Issue 728, Pages 35–63, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle-2014-0114.

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