Journal of the American Mathematical Society

Author(s): Chiu-Chu Melissa Liu; Kefeng Liu; Jian Zhou
Journal: J. Amer. Math. Soc. 20 (2007), 149-184.
MSC (2000): Primary 14N35, 53D45; Secondary 57M27
Posted: 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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Retrieve articles in Journal of the American Mathematical Society with MSC (2000): 14N35, 53D45, 57M27

Chiu-Chu Melissa Liu
Affiliation: Center of Mathematical Sciences, Zhejiang University, Hangzhou, Zhejiang 310027, People's Republic of China and Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
Address at time of publication: Department of Mathematics, Columbia University, New York, New York, 10027
Email: ccliu@math.columbia.edu

Kefeng Liu
Affiliation: Center of Mathematical Sciences, Zhejiang University, Hangzhou, Zhejiang 310027, People's Republic of China and Department of Mathematics, University of California at Los Angeles, Los Angeles, California 90095-1555
Email: liu@cms.zju.edu.cn, liu@math.ucla.edu

Jian Zhou
Affiliation: Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, People's Republic of China and Center of Mathematical Sciences, Zhejiang University, Hangzhou, Zhejiang 310027, People's Republic of China
Email: jzhou@math.tsinghua.edu.cn

DOI: 10.1090/S0894-0347-06-00541-8
PII: S 0894-0347(06)00541-8
Keywords: Hodge integrals, localization, Gromov-Witten invariants, Hopf link
Received by editor(s): January 19, 2005
Posted: August 1, 2006
Copyright of article: Copyright 2006, American Mathematical Society

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ISSN: 1088-6834(e) ISSN: 0894-0347(p)

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