Recursion formulae of higher Weil-Petersson volumes

Details Recursion formulae of higher Weil-Petersson volumes Recursion formulae of higher Weil-Petersson volumes

2007-08-03

arxiv.org/abs/0708.0565v2

Int. Math. Res. Notices (2009) 2009 (5): 835-859

Mathematics

Algebraic Geometry

18 pages, to appear in IMRN

Scientific paper

In this paper we study effective recursion formulae for computing intersection numbers of mixed $\psi$ and $\kappa$ classes on moduli spaces of curves. By using the celebrated Witten-Kontsevich theorem, we generalize Mulase-Safnuk form of Mirzakhani's recursion and prove a recursion formula of higher Weil-Petersson volumes. We also present recursion formulae to compute intersection pairings in the tautological rings of moduli spaces of curves.

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