Year: 2002
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Kokotov, A., Korotkin, D.
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2951912508