Journal of Algebraic Geometry

Author(s): Chiu-Chu Melissa Liu; Kefeng Liu; Jian Zhou
Journal: J. Algebraic Geom. 15 (2006), 379-398.
Posted: September 7, 2005
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Abstract: We derive some Hodge integral identities by taking various limits of the Mariño-Vafa formula using the cut-and-join equation. These identities include the formula of general $\lambda_g$ -integrals, the formula of $\lambda_{g-1}$ -integrals on ${\overline{\mathcal{M}}}_{g,1}$ , the formula of cubic $\lambda$ integrals on ${\overline{\mathcal{M}}}_g$ , and the ELSV formula relating Hurwitz numbers and Hodge integrals. In particular, our proof of the MV formula by the cut-and-join equation leads to a new and simple proof of the $\lambda_g$ conjecture. We also present a proof of the ELSV formula completely parallel to our proof of the Mariño-Vafa formula.

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Chiu-Chu Melissa Liu
Affiliation: Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138 and Center of Mathematical Sciences, Zhejiang University, Hangzhou, Zhejiang 310027, China
Address at time of publication: Department of Mathematics, Northwestern University, Evanston, Illinois 60208-2370
Email: ccliu@math.harvard.edu, ccliu@math.northwestern.edu

Kefeng Liu
Affiliation: Center of Mathematical Sciences, Zhejiang University, Hangzhou, Zhejiang 310027, 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: Center of Mathematical Sciences, Zhejiang University, Hangzhou, Zhejiang 310027, China and Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
Email: jzhou@math.tsinghua.edu.cn

PII: S 1056-3911(05)00419-4
Received by editor(s): March 15, 2005
Posted: September 7, 2005

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