Flat metrics with conical singularities on
and determinants of Laplacians
Flat metrics with conical singularities on compact Riemann surfaces are
The metrics are given as the 2/n-th power of the modulus of holomorphic
Our goal is to calculate the
zeta-regularized determinants of the Laplacians corresponding to
The determinant of the Laplacian essentially
coincides (up to a simple factor) with the modulus squared of a
holomorphic function on the moduli space of n-differentials.
This function turns out to be a complete analog
of the isomonodromic tau-function of Hurwitz Frobenius manifolds.