Curve counting and instanton counting

Abstract

We prove some combinatorial results required for the proof of the following conjecture of Nekrasov: The generating function of closed string invariants in local Calabi-Yau geometries obtained by appropriate fibrations of $A_N$ singularities over $P^1$ reproduce the generating function of equivariant $\hat{A}$-genera of moduli space of instants on $C^2$.

References in corpus (3)

• Hodge integrals, Hurwitz numbers, and Symmetric Groups
• A Conjecture on Hodge Integrals
• Localizations on Moduli Spaces and Free Field Realizations of Feynman Rules

Cited by in corpus (1)

• A simple proof of Gopakumar-Vafa conjecture for local toric Calabi-Yau manifolds