3 years ago

# Stieltjes–Bethe equations in higher genus and branched coverings with even ramifications

We describe projective structures on a Riemann surface corresponding to monodromy groups which have trivial $S L ( 2 )$ monodromies around singularities and trivial $P S L ( 2 )$ monodromies along homologically non-trivial loops on a Riemann surface. We propose a natural higher genus analog of Stieltjes–Bethe equations. Links with branched projective structures and with Hurwitz spaces with ramifications of even order are established. We find a higher genus analog of the genus zero Yang–Yang function (the function generating accessory parameters) and describe its similarity and difference with Bergman tau-function on the Hurwitz spaces.

Publisher URL: www.sciencedirect.com/science

DOI: S0550321317304108

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