JournalsprimsVol. 42 , No. 2DOI 10.2977/prims/1166642118

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

  • Yukiko Konishi

    Kyoto University, Japan
Integrality of Gopakumar–Vafa Invariants of Toric Calabi–Yau Threefolds cover

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.