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Hodge Integrals and Hurwitz Numbers via Virtual Localization

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Compositio Mathematica

Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Harvard University, Cambridge, MA, 02138, U.S.A

    Tom Graber

  2. Department of Mathematics, Stanford University Bldg. 380, Stanford, CA, 94305–2125, U.S.A.

    Ravi Vakil

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  1. Tom Graber
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  2. Ravi Vakil
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Graber, T., Vakil, R. Hodge Integrals and Hurwitz Numbers via Virtual Localization. Compositio Mathematica 135, 25–36 (2003). https://doi.org/10.1023/A:1021791611677

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