Recursion Formulae of Higher Weil-Petersson Volumes

Abstract

In this paper, we study effective recursion formulae for computing intersection numbers of mixed and 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.