New results of intersection numbers on moduli spaces of curves

Details New results of intersection numbers on moduli spaces of curves New results of intersection numbers on moduli spaces of curves

2007-05-24

arxiv.org/abs/0705.3564v1

Proc.Nat.Acad.Sci.104:13896-13900,2007

Mathematics

Algebraic Geometry

9 pages, a brief survey

Scientific paper

10.1073/pnas.0705910104

We present a series of new results we obtained recently about the intersection numbers of tautological classes on moduli spaces of curves, including a simple formula of the n-point functions for Witten's $\tau$ classes, an effective recursion formula to compute higher Weil-Petersson volumes, several new recursion formulae of intersection numbers and our proof of a conjecture of Itzykson and Zuber concerning denominators of intersection numbers. We also present Virasoro and KdV properties of generating functions of general mixed $\kappa$ and $\psi$ intersections.

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