Note on a Conjecture of Gopakumar-Vafa

Abstract

We rephrase the Gopakumar-Vafa conjecture on genus zero Gromov-Witten invariants of Calabi-Yau threefolds in terms of the virtual degree of the moduli of pure dimension one stable sheaves and investigate the conjecture for K3 fibred local Calabi-Yau threefolds.

Keywords

Calabi-Yau threefold / Gromov-Witten invariants / Moduli of stable sheaves / 14D20 / 14D21 / 14J30 / 14N35

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