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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.
