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

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

2004-05-04

arxiv.org/abs/math/0405042v5

Mathematics

Spectral Theory

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

Scientific paper

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
$g=1$.

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