Tau-functions on spaces of Abelian differentials and higher genus generalizations of Ray-Singer formula
Abstract
Description
Let $w$ be an Abelian differential on compact Riemann surface of genus $g\geq 1$. We obtain an explicit holomorphic factorization formula for $ζ$-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
53 pages; the paper in present form is essentally self-contained; the proofs are improved