Unramified Gromov-Witten and Gopakumar-Vafa invariants

2024/05/28 by Nesterov, Denis
#Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2405.18398

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.

Related

• The Gopakumar-Vafa formula for symplectic manifolds
• Gopakumar-Vafa invariants via vanishing cycles
• Gromov-Witten, Gopakumar-Vafa, and Donaldson-Thomas invariants of Calabi-Yau threefolds
• A note on BPS structures and Gopakumar-Vafa invariants
• Integrality of Gopakumar-Vafa Invariants of Toric Calabi-Yau Threefolds