Tau function and moduli of differentials
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Publication:5415261
zbMATH Open1291.34156arXiv1003.2173MaRDI QIDQ5415261
Publication date: 12 May 2014
Abstract: The tau function on the moduli space of generic holomorphic 1-differentials on complex algebraic curves is interpreted as a section of a line bundle on the projectivized Hodge bundle over the moduli space of stable curves. The asymptotics of the tau function near the boundary of the moduli space of 1-differentials is computed, and an explicit expression for the pullback of the Hodge class on the projectivized Hodge bundle in terms of the tautological class and the classes of boundary divisors is derived. This expression is used to clarify the geometric meaning of the Kontsevich-Zorich formula for the sum of the Lyapunov exponents associated with the Teichm"uller flow on the Hodge bundle.
Full work available at URL: https://arxiv.org/abs/1003.2173
Families, moduli of curves (algebraic) (14H10) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35)
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