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Hodge integrals and Hurwitz numbers via virtual localization

Tom Graber·Ravi Vakil
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Abstract

Ekedahl, Lando, Shapiro, and Vainshtein announced a remarkable formula expressing Hurwitz numbers (counting covers of the projective line with specified simple branch points, and specified branching over one other point) in terms of Hodge integrals. We give a proof of this formula using virtual localization on the moduli space of stable maps, and describe how the proof could be simplified by the proper algebro-geometric definition of a "relative space".

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Tom Graber, Ravi Vakil. 2000-03-03. Hodge integrals and Hurwitz numbers via virtual localization. https://arxiv.org/abs/math/0003028

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