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Holomorphic and de Rham torsion

Published online by Cambridge University Press:  04 December 2007

Jean-Michel Bismut
Jean-Michel Bismut
Affiliation:
Département de Mathématique, Université Paris-Sud, Bâtiment 425, 91405 Orsay, FranceJean-Michel.Bismut@math.u-psud.fr
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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.

Keywords

analytic torsion formsindex theory58J52 (primary)58J20 (secondary)
Type
Research Article
Information
Compositio Mathematica , Volume 140 , Issue 5 , September 2004 , pp. 1302 - 1356
Copyright
Foundation Compositio Mathematica 2004