Some results of the Mariño-Vafa formula

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.

Full Text (PDF format)

Published 1 January 2006