Abstract
In this paper, we derive the main properties of Kähler fibrations. We introduce the associated Levi-Civita superconnection to construct analytic torsion forms for holomorphic direct images. These forms generalize in any degree the analytic torsion of Ray and Singer. In the case of acyclic complexes of holomorphic Hermitian vector bundles, such forms are calculated by means of Bott-Chern classes.
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Communicated by A. Jaffe
Supported by NSF Grant DMS 850248 and by the Sloan Foundation
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Bismut, JM., Gillet, H. & Soulé, C. Analytic torsion and holomorphic determinant bundles. Commun.Math. Phys. 115, 79–126 (1988). https://doi.org/10.1007/BF01238854
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DOI: https://doi.org/10.1007/BF01238854