Variation of the holomorphic determinant bundle

TL;DR

This paper proves that the determinant of cohomology for holomorphic vector bundles remains invariant under deformation, using the Grothendieck-Riemann-Roch formula in Deligne cohomology.

Contribution

It establishes the deformation invariance of the holomorphic determinant bundle via a cohomological formula, extending previous results.

Findings

Invariance of the determinant of cohomology under bundle deformation

Application of Grothendieck-Riemann-Roch in Deligne cohomology

Extension of classical invariance results

Abstract

In this paper, we prove that the Grothendieck-Riemann-Roch formula in Deligne cohomology computing the determinant of the cohomology of a holomorphic vector bundle on the fibers of a proper submersion between abstract complex manifolds is invariant by deformation of the bundle.