Degenerating Riemann Surfaces and the Quillen Metric
Journal article, 2013

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.

space

curves

singularities

discriminant

dual varieties

bundles

Author

Dennis Eriksson

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

International Mathematics Research Notices

1073-7928 (ISSN) 1687-0247 (eISSN)

2 347-361

Subject Categories

Mathematics

DOI

10.1093/imrn/rnr234

More information

Created

10/8/2017