Unramified Gromov-Witten and Gopakumar-Vafa invariants

TL;DR

This paper proves a conjecture relating unramified Gromov-Witten invariants to Gopakumar-Vafa invariants for certain threefold classes, using wall-crossing techniques to provide an algebraic geometric construction.

Contribution

It establishes the equality of unramified Gromov-Witten and Gopakumar-Vafa invariants for Fano and primitive Calabi-Yau classes on threefolds, confirming a conjecture.

Findings

Proves the conjecture using wall-crossing techniques

Provides an algebraic geometric construction of Gopakumar-Vafa invariants

Establishes equality for Fano and primitive Calabi-Yau classes

Abstract

Kim, Kresch and Oh defined unramified Gromov-Witten invariants. For a threefold, Pandharipande conjectured that they are equal to Gopakumar-Vafa invariants (BPS invariants) in the case of Fano classes and primitive Calabi-Yau classes. We prove the conjecture using a wall-crossing technique. This provides an algebro-geometric construction of Gopakumar-Vafa invariants in these cases.