Integrality of Gopakumar-Vafa Invariants of Toric Calabi-Yau Threefolds

2005/04/10 by Yukiko Konishi, Konishi, Yukiko · 1 citation
Mathematics · #05E05 #14N35 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.math/0504188

openalex publication_date 2005/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Gopakumar-Vafa invariants are numbers defined as certain linear combinations of the Gromov-Witten invariants. We prove that the GV invariants of a toric Calabi-Yau threefold are integers and that the invariants for high genera vanish. The proof of the integrality is based on elementary number theory and that of the vanishing uses the operator formalism and the exponential formula.

Citations

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

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• Multi-Component Open/Relative/Local Correspondence

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