The Hurwitz Enumeration Problem of Branched Covers and Hodge Integrals

Details The Hurwitz Enumeration Problem of Branched Covers and Hodge Integrals The Hurwitz Enumeration Problem of Branched Covers and Hodge Integrals

2000-09-15

arxiv.org/abs/hep-th/0009129v1

J.Geom.Phys. 50 (2004) 223-256

Physics

High Energy Physics

High Energy Physics - Theory

35 pages, no figures

Scientific paper

We use algebraic methods to compute the simple Hurwitz numbers for arbitrary source and target Riemann surfaces. For an elliptic curve target, we reproduce the results previously obtained by string theorists. Motivated by the Gromov-Witten potentials, we find a general generating function for the simple Hurwitz numbers in terms of the representation theory of the symmetric group S_n. We also find a generating function for Hodge integrals on the moduli space M_{g,2} of Riemann surfaces with two marked points, similar to that found by Faber and Pandharipande for the case of one marked point.

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