2002/02/25 by Alexey Kokotov, A. Kokotov, Kokotov, A. +2
Mathematics · Physics and Astronomy · #32G99 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Physical sciences #Holomorphic and Operator Theory #Mathematical Physics (math-ph) #math-ph #math.MP #msc:32G99
paper · pdf · doi:10.48550/arxiv.math-ph/0202034
Substantial expansion; higher genus case is added
openalex publication_date 2002/02/25 · arxiv created 2003/02/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.