Journal
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
Volume 96, Issue 5, Pages 462-483Publisher
GAUTHIER-VILLARS/EDITIONS ELSEVIER
DOI: 10.1016/j.matpur.2011.04.003
Keywords
Hodge modules; Symmetric products; Cohomology sheaves
Categories
Funding
- Kakenhi [21540037]
- [NSF-1005338]
- [SFB 878]
- Grants-in-Aid for Scientific Research [21540037] Funding Source: KAKEN
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Generalizing a theorem of Macdonald, we show a formula for the mixed Hodge structure on the cohomology of the symmetric products of bounded complexes of mixed Hodge modules by showing the existence of the canonical action of the symmetric group on the multiple external self-products of complexes of mixed Hodge modules. We also generalize a theorem of Hirzebruch and Zagier on the signature of the symmetric products of manifolds to the case of the symmetric products of symmetric pairings on bounded complexes with constructible cohomology sheaves where the pairing is not assumed to be non-degenerate. (C) 2011 Elsevier Masson SAS. All rights reserved.
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