Tau-functions on spaces of Abelian and quadratic differentials and determinants of Laplacians in Strebel metrics of finite volume

Dmitry Korotkin and Alexey Kokotov

Contact the author: Please use for correspondence this email.
Submission date: 20. Jul. 2004
Pages: 48
Bibtex
Keywords and phrases: spaces of holomorphic differentials, determinants of the laplacians, bergman projective connection
Download full preprint: PDF (487 kB), PS ziped (329 kB)

Abstract:
We define and explicitly calculate the tau-functions on different strata of spaces of Abelian and quadratic differentials. This provides a machinery to calculate the determinants of Laplacians in flat metrics with conical singularities on Riemann surfaces. The results can be considered as a generalization of the famous Kronecker formula for the Laplacian in the flat metric on an elliptic surface to the case of higher genus.