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Tau-functions on spaces of Abelian and quadratic differentials and determinants of Laplacians in Strebel metrics of finite volume
Dmitry Korotkin and Alexey Kokotov
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.