2015/11/15 by Martin Puchol, Puchol, Martin
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1511.04694
openalex publication_date 2015/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The purpose of this paper is first to give an asymptotic formula for the holomorphic analytic torsion forms of a fibration associated with increasing powers of a given line bundle. Secondly, we generalize this formula, thanks to the theory of Toeplitz operators, in the case where the powers of the line bundle is replaced by the direct image of powers of a line bundle on a bigger manifold. In both cases we have to make fiberwise positivity assumption on the line bundle. This results are the family versions of the results of Bimsut and Vasserot on the asymptotic of the holomorphic torsion.