Physics – Mathematical Physics
Scientific paper
2002-02-25
Physics
Mathematical Physics
Substantial expansion; higher genus case is added
Scientific paper
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.
Kokotov Alexey
Korotkin Dmitrii
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