Analytic torsion forms for fibrations by projective curves

TL;DR

This paper derives explicit formulas for analytic torsion forms in fibrations by projective curves, facilitating computations in Arakelov geometry and introducing a novel description of Bismut's equivariant Bott-Chern current for isolated fixed points.

Contribution

It provides a new explicit formula for analytic torsion forms in fibrations by projective curves and a novel description of Bismut's equivariant Bott-Chern current for isolated fixed points.

Findings

Explicit formula for analytic torsion forms in fibrations by projective curves

Application to direct images in Arakelov geometry

New description of Bismut's equivariant Bott-Chern current

Abstract

An explicit formula for analytic torsion forms for fibrations by projective curves is given. In particular one obtains a formula for direct images in Arakelov geometry in the corresponding setting. The main tool is a new description of Bismut's equivariant Bott-Chern current in the case of isolated fixed points.