The asymptotics of the holomorphic analytic torsion forms

Abstract

The purpose of this paper is to give an asymptotic formula for the holomorphic analytic torsion forms of a fibration associated with a sequence of direct images of increasing powers of a line bundle on a bigger manifold. To handle the growing dimension of the direct images, we use the theory of Toeplitz operators. This is the family versions of the results of Bimsut and Vasserot on the asymptotics of the holomorphic torsion, as well an extension for more general bundles.