The n-point functions for intersection numbers on moduli spaces of curves

Abstract

Using the celebrated Witten-Kontsevich theorem, we prove a recursive formula of the $n$-point functions for intersection numbers on moduli spaces of curves. It has been used to prove the Faber intersection number conjecture and motivated us to find some conjectural vanishing identities for Gromov-Witten invariants. The latter has been proved recently by X. Liu and R. Pandharipande. We also give a combinatorial interpretation of $n$-point functions in terms of summation over binary trees.

22 pages

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Cited by in corpus (9)

• Intersection numbers of spectral curves
• Descendent integrals and tautological rings of moduli spaces of curves
• BKP Hierarchy, Affine Coordinates, and a Formula for Connected Bosonic $N$-Point Functions
• An effective recursion formula for computing intersection numbers
• New topological recursion relations
• Intersection numbers and automorphisms of stable curves
• A proof of the Faber intersection number conjecture
• New properties of the intersection numbers on moduli spaces of curves
• A remark on Mirzakhani's asymptotic formulae