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MiS Preprint
46/2004

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

Dmitry Korotkin and Alexey Kokotov

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.

Received:
Jul 20, 2004
Published:
Jul 20, 2004
Keywords:
spaces of holomorphic differentials, determinants of the laplacians, bergman projective connection

Related publications

Preprint
2004 Repository Open Access
Dmitry Korotkin and Alexey Kokotov

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