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

A. Kokotov·I. A. B. Strachan
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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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A. Kokotov, I. A. B. Strachan. 2004-02-19. On the isomonodromic tau-function for the Hurwitz spaces of branched coverings of genus zero and one. https://doi.org/10.4310/mrl.2005.v12.n6.a7

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