Gopakumar–Vafa Invariants of $\mathcal {O}(k)\oplus \mathcal {O}(-k-2)$

Shuai Guo, Ting Zhang

School of Mathematical Sciences, Peking University, Beijing, 100871, China

Abstract: We prove a closed formula for the leading Gopakumar–Vafa invariants of local Calabi–Yau threefolds of $\mathcal {O}(k)\oplus \mathcal {O}(-k-2)\to \mathbb {P}^1$ by the topological vertex. We also obtain some results that were not previously predicted.

Keywords: local Gromov–Witten invariants, Calabi–Yau threefolds, Gopakumar–Vafa invariants.

Received: May 5, 2025
Revised: June 20, 2025
Accepted: October 2, 2025

DOI: 10.4213/tm4512

 English version: Proceedings of the Steklov Institute of Mathematics, 2025, 330, 153–175

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