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# Mathematical Research Letters

## Volume 13 (2006)

### Number 6

### Some results of the Mariño-Vafa formula

Pages: 847 – 864

DOI: http://dx.doi.org/10.4310/MRL.2006.v13.n6.a2

#### Author

#### Abstract

In this paper we derive some new Hodge integral identities by taking the limits of Mariño-Vafa formula. These identities include the formula of $\lambda_{1}\lambda_{g}$-integral on $\overline{\sM}_{g,1}$, the vanishing result of $\lambda_{g}{\rm ch}_{2l}(\E)$-integral on $\overline{\sM}_{g,1}$ for $1\leq l\leq g-3$. Using the differential equation of Hodge integrals, we give a recursion formula of $\lambda_{g-1}$-integrals. Finally, we give two simple proofs of $\lambda_{g}$ conjecture and some examples of low genus integral.