Mathematical Research Letters

Volume 14 (2007)

Number 6

New properties of the intersection numbers on moduli spaces of curves

Pages: 1041 – 1054

DOI: http://dx.doi.org/10.4310/MRL.2007.v14.n6.a12

Authors

Kefeng Liu (Zhejiang University)

Hao Xu (Zhejiang University)

Abstract

We present certain new properties about the intersection numbers on moduli spaces of curves $\overline{\sM}_{g,n}$, including a simple explicit formula of $n$-point functions and several new identities of intersection numbers. In particular we prove a new identity, which together with a conjectural identity implies the famous Faber’s conjecture about relations in $\mathcal R^{g-2}(\sM_g)$. These new identities clarify the mysterious constant in Faber’s conjecture and uncover novel combinatorial structures of intersection numbers. We also discuss some numerical properties of Hodge integrals which have provided numerous inspirations for this work.

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