The asymptotics of the holomorphic analytic torsion forms

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.

Automated summary

The purpose of this paper is to provide 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 deal with the increasing dimension of the direct images, the theory of Toeplitz operators is utilized. This work extends the results of Bimsut and Vasserot on the asymptotics of the holomorphic torsion to more general bundles.