Hodge Integrals and Hurwitz Numbers via Virtual Localization
Source: Compositio Mathematica, Volume 135, Number 1, January 2003 , pp. 25-36(12)
We give another proof of Ekedahl, Lando, Shapiro, and Vainshtein's remarkable formula expressing Hurwitz numbers (counting covers of P1 with specified simple branch points, and specified branching over one other point) in terms of Hodge integrals. Our proof uses virtual localization on the moduli space of stable maps. We describe how the proof could be simplified by the proper algebro-geometric definition of a ‘relative space’. Such a space has recently been defined by J. Li.
Document Type: Research Article
Affiliations: 1: Department of Mathematics, Harvard University, Cambridge MA 02138, U.S.A. e-mail: firstname.lastname@example.org 2: Department of Mathematics, Stanford University Bldg. 380, Stanford CA 94305–2125, U.S.A. e-mail: email@example.com
Publication date: January 2003