A formula of two-partition Hodge integrals

Liu, Chiu-Chu Melissa; Liu, Kefeng; Zhou, Jian

doi:10.1090/S0894-0347-06-00541-8

A formula of two-partition Hodge integrals
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by Chiu-Chu Melissa Liu, Kefeng Liu and Jian Zhou

J. Amer. Math. Soc. 20 (2007), 149-184

DOI: https://doi.org/10.1090/S0894-0347-06-00541-8

Published electronically: August 1, 2006

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Abstract:

Motivated by the Mariño-Vafa formula of Hodge integrals and physicists’ predictions on local Gromov-Witten invariants of toric Fano surfaces in a Calabi-Yau threefold, the third author conjectured a formula of certain Hodge integrals in terms of certain Chern-Simons invariants of the Hopf link. We prove this formula by virtual localization on moduli spaces of relative stable morphisms.

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