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

Abstract

Let $w$ be an Abelian differential on compact Riemann surface of genus $g\ge 1$. 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 $g=1$.

53 pages; the paper in present form is essentally self-contained; the proofs are improved

References in corpus (1)

• Connected components of the moduli spaces of Abelian differentials with prescribed singularities

Cited by in corpus (1)

• Measures on Banach Manifolds, Random Surfaces, and Nonperturbative String Field Theory with Cut-offs