. A G ] 1 4 M ar 2 00 5 MARIÑO - VAFA FORMULA AND HODGE INTEGRAL IDENTITIES

نویسنده

  • JIAN ZHOU
چکیده

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 λg-integrals, the formula of λg−1-integrals on Mg,1, the formula of cubic λ integrals on Mg, 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 λg conjecture. We also present a proof of the ELSV formula completely parallel to our proof of the Mariño-Vafa formula.

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تاریخ انتشار 2008