# MathSciDoc: An Archive for Mathematician ∫

#### Algebraic Geometrymathscidoc:1912.43060

International Mathematics Research Notices, 2009, (5), 835-859, 2009
In this paper, we study effective recursion formulae for computing intersection numbers of mixed \psi and \psi classes on moduli spaces of curves. By using the celebrated WittenKontsevich theorem, we generalize MulaseSafnuk form of Mirzakhani's recursion and prove a recursion formula of higher WeilPetersson volumes. We also present recursion formulae to compute intersection pairings in the tautological rings of moduli spaces of curves.
@inproceedings{kefeng2009recursion,
title={Recursion formulae of higher WeilPetersson volumes},
author={Kefeng Liu, and Hao Xu},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111318815008620},
booktitle={International Mathematics Research Notices},
volume={2009},
number={5},
pages={835-859},
year={2009},
}

Kefeng Liu, and Hao Xu. Recursion formulae of higher WeilPetersson volumes. 2009. Vol. 2009. In International Mathematics Research Notices. pp.835-859. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111318815008620.