The Hurwitz enumeration problem of branched covers and Hodge integrals

Stefano Monni, Jun S. Song, Yun S. Song

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)223-256
Number of pages34
JournalJournal of Geometry and Physics
Issue number1-4
StatePublished - Apr 2004
Externally publishedYes


  • Descendant Gromov-Witten invariants
  • Generating functions
  • Hodge integrals
  • Hurwitz numbers

ASJC Scopus subject areas

  • Mathematical Physics
  • General Physics and Astronomy
  • Geometry and Topology


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