Tau-functions on spaces of Abelian differentials and higher genus generalizations of Ray-Singer formula

By A. Kokotov, Dmitry Korotkin. 2004

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Let $w$ be an Abelian differential on compact Riemann surface of genus $g\geq 1$. We obtain an explicit holomorphic factorization formula for $\zeta$-regularized determinant of the Laplacian in flat conical metrics with trivial holonomy $|w|^2$, generalizing the classical Ray-Singer result in $g=1$.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/24f35a46fede63ef95c2f2606e84c344712b98f2