New properties of the intersection numbers on moduli spaces of curves

Details New properties of the intersection numbers on moduli spaces of curves New properties of the intersection numbers on moduli spaces of curves

2006-09-14

arxiv.org/abs/math/0609367v5

Math. Res. Letter 14 (2007), no. 6, 1041--1054

Mathematics

Algebraic Geometry

14 pages, added a new section, to appear in Math. Res. Letter

Scientific paper

We present certain new properties about the intersection numbers on moduli spaces of curves $\bar{\sM}_{g,n}$, 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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