Isomonodromic deformations and Hurwitz spaces

Abstract

A class of Riemann-Hilbert problems corresponding to quasi-permutation monodromy matrices is solved in terms of Szeg\"o kernel on auxiliary Riemann surfaces. The tau-function of Schlesinger system turns out to be closely related to determinant of Cauchy-Riemann operator. The link between theta-divisor and Malgrange's divisor in the theory of Schlesinger equations is established.