Tau-functions on spaces of Abelian and quadratic differentials and determinants of Laplacians in Strebel metrics of finite volume
نویسنده
چکیده
2 Tau-function on spaces of Abelian differentials over Riemann surfaces 7 2.1 Spaces of holomorphic differentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Variational formulas on Hg(k1, . . . , kM ) . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 Basic Beltrami differentials for Hg(k1, . . . , kM ) . . . . . . . . . . . . . . . . . . . . . . 11 2.4 Definition of the Bergman tau-function . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.5 Differential C and its variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.6 Dirichlet integral: variational formulas and holomorphic factorization . . . . . . . . . . 14 2.6.1 Holomorphic factorization of the Dirichlet integral . . . . . . . . . . . . . . . . 15 2.6.2 Variation of the Dirichlet integral . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.7 Explicit formula for the Bergman tau-function . . . . . . . . . . . . . . . . . . . . . . 20 2.8 Tau-function on Hurwitz spaces and G-function of Hurwitz Frobenius manifolds . . . . 22
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Tau-functions on spaces of holomorphic differentials over Riemann surfaces and determinants of Laplacians in flat metrics with conic singularities over Riemann surfaces
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تاریخ انتشار 2008