Symmetric products of mixed Hodge modules

By Laurentiu G. Maxim, Morihiko Saito, Joerg Schuermann. 2010

51 citations recorded by the source corpus.

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 parings on bounded complexes with constructible cohomology sheaves where the pairing is not assumed to be non-degenerate.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bb413888be81742c5e3c61695bc182cfa6398ffa

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In Geometry and Topology

1. Ben Davison
2. Junliang Shen
3. Davesh Maulik

In Mathematical Physics

1. Ben Davison
2. Junliang Shen
3. Davesh Maulik

Citations in the corpus

• The integrality conjecture and the cohomology of preprojective stacks (2016, background): “ As above, we let πζ f,d: M(Q) ζ f,d → M(Q) ζ -ss d be the forgetful map taking a stable framed ζ-semistable representation to its underlying ζ-polystable representation. Then there is an isomorphism (22) πζ f,d,!φ mon T r(W)ζ f ,d QM(Q)ζ f d ∼= H πζ f,d,!φ mon T r(W)ζ f,d QM(Q)ζ , i.e. the left h”