Abstract
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 Sn. We also find a generating function for Hodge integrals on the moduli space M̄g,2 of Riemann surfaces with two marked points, similar to that found by Faber and Pandharipande for the case of one marked point.
Original language | English (US) |
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Pages (from-to) | 223-256 |
Number of pages | 34 |
Journal | Journal of Geometry and Physics |
Volume | 50 |
Issue number | 1-4 |
DOIs | |
State | Published - Apr 2004 |
Externally published | Yes |
Keywords
- Descendant Gromov-Witten invariants
- Generating functions
- Hodge integrals
- Hurwitz numbers
ASJC Scopus subject areas
- Mathematical Physics
- General Physics and Astronomy
- Geometry and Topology