Open AccessThe asymptotics of the holomorphic torsion forms
Author(s) -
Martin Puchol
Publication year - 2016
Publication title -
comptes rendus mathématique
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.803
H-Index - 68
eISSN - 1778-3569
pISSN - 1631-073X
DOI - 10.1016/j.crma.2015.11.004
Subject(s) - holomorphic function , mathematics , torsion (gastropod) , toeplitz matrix , pure mathematics , vector bundle , medicine , surgery
In this note, we use the theory of Toeplitz operators to give an asymptotic formula for the holomorphic analytic torsion forms associated with a family of holomorphic vector bundles that are the direct image of L⊗p, where L is a line bundle. To obtain the asymptotics, we make a positivity assumption along the fibers on L. This result is the family version of the results of Bismut and Vasserot on the holomorphic torsion
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