Degenerating Riemann surfaces and the Quillen metric
Algebraic Geometry
2011-06-17 v1
Abstract
The degeneration of the Quillen metric for a one-parameter family of Riemann surfaces has been studied by Bismut-Bost and Yoshikawa. In this article we propose a more geometric point of view using Deligne's Riemann-Roch theorem. We obtain an interpretation of the singular part of the metric as a discriminant and the continuous part as a degeneration of the metric on Deligne products, which gives an asymptotic development involving the monodromy eigenvalues. This generalizes the results of Bismut-Bost and is a version of Yoshikawa's results on the degeneration of the Quillen metric for general degenerations with isolated singularities in the central fiber.
Keywords
Cite
@article{arxiv.1106.3092,
title = {Degenerating Riemann surfaces and the Quillen metric},
author = {Dennis Eriksson},
journal= {arXiv preprint arXiv:1106.3092},
year = {2011}
}