Mathematical Research Letters

Volume 12 (2005)

Number 6

On the isomonodromic tau-function for the Hurwitz spaces of branched coverings of genus zero and one

Pages: 857 – 876

DOI: http://dx.doi.org/10.4310/MRL.2005.v12.n6.a7

Authors

Alexey Kokotov (Concordia University, Canada)

Ian A. B. Strachan (University of Glasgow)

Abstract

The isomonodromic tau-function for the Hurwitz spaces of branched coverings of genus zero and one are constructed explicitly. Such spaces may be equipped with the structure of a Frobenius manifold and this introduces a flat coordinate system on the manifold. The isomonodromic tau-function, and in particular the associated $G$-function, are rewritten in these coordinates and an interpretation in terms of the caustics (where the multiplication is not semisimple) is given.

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