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Tau-function on Hurwitz spaces

A. Kokotov·D. Korotkin
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Abstract

We construct a flat holomorphic line bundle over a connected component of the Hurwitz space of branched coverings of the Riemann sphere. A flat holomorphic connection defining the bundle is described in terms of the invariant Wirtinger projective connection on the branched covering corresponding to a given meromorphic function on a Riemann surface. In genera 0 and 1 we construct a nowhere vanishing holomorphic horizontal section of this bundle (the ``Wirtinger tau-function''). In higher genus we compute the modulus square of the Wirtinger tau-function.

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A. Kokotov, D. Korotkin. 2003-02-10. Tau-function on Hurwitz spaces. https://arxiv.org/abs/math-ph/0202034

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