2003/10/07 by Alexey Kokotov, A. Kokotov, Kokotov, A. +2
Mathematics · Physics and Astronomy · #34M55 #53D45 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #math-ph #math.MP #msc:34M55 #msc:53D45 #nlin.SI
paper · pdf · doi:10.48550/arxiv.math-ph/0310008
The direct proof of variational formulas on branched coverings is added. The title is modified due to observed coincidence of isomonodromic tau-function of Hurwitz Frobenius manifolds with Bergman tau-function on Hurwitz spaces introduced by the authors
openalex publication_date 2003/10/07 · arxiv created 2005/03/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work we find the isomonodromic (Jimbo-Miwa) tau-function corresponding to Frobenius manifold structures on Hurwitz spaces. We discuss several applications of this result. First, we get an explicit expression for the G-function (solution of Getzler's equation) of the Hurwitz Frobenius manifolds. Second, in terms of this tau-function we compute the genus one correction to the free energy of hermitian two-matrix model. Third, we find the Jimbo-Miwa tau-function of an arbitrary Riemann-Hilbert problem with quasi-permutation monodromy matrices. Finally, we get a new expression (analog of genus one Ray-Singer formula) for the determinant of Laplace operator in the Poincaré metric on Riemann surfaces of an arbitrary genus.