Isomonodromic deformations and Hurwitz spaces

Details Isomonodromic deformations and Hurwitz spaces Isomonodromic deformations and Hurwitz spaces

2001-03-18

arxiv.org/abs/math-ph/0103023v1

Physics

Mathematical Physics

To appear in "Isomonodromy deformations and applications", ed. by J.Harnad and A.Its, CRM proceedings, AMS (2001)

Scientific paper

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.

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