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Holomorphic and de Rham torsion

Published online by Cambridge University Press:  04 December 2007

Jean-Michel Bismut
Affiliation:
Département de Mathématique, Université Paris-Sud, Bâtiment 425, 91405 Orsay, [email protected]
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Abstract

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We prove the vanishing of the equivariant holomorphic torsion forms associated to the holomorphic de Rham complex. We also consider corresponding torsion forms associated to complexes in hypercohomology, for which we give a local formula. Rigidity of certain genera explains part of these formulas. The Lefschetz operators in Hodge theory play a prominent role in the proofs.

Type
Research Article
Copyright
Foundation Compositio Mathematica 2004