Curve counting and instanton counting
Jian Zhou

TL;DR
This paper proves combinatorial results supporting Nekrasov's conjecture that relates string invariants in certain Calabi-Yau geometries to equivariant genera of instanton moduli spaces, bridging geometry and physics.
Contribution
It establishes key combinatorial foundations necessary for proving Nekrasov's conjecture linking string invariants and instanton moduli space genera.
Findings
Proved combinatorial results for Nekrasov's conjecture
Connected string invariants with equivariant $\hat{A}$-genera
Supported the geometric-physical correspondence in Calabi-Yau geometries
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 singularities over reproduce the generating function of equivariant -genera of moduli space of instants on .
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Taxonomy
TopicsBlack Holes and Theoretical Physics · Geometry and complex manifolds · Geometric Analysis and Curvature Flows
