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Note on a Conjecture of Gopakumar-Vafa

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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.

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Correspondence to Jun Li*.

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(Dedicated to the memory of Shiing-Shen Chern)

*Partially supported by NSF grants DMS-0200477 and DMS-0233550.

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Li*, J., Wu, B. Note on a Conjecture of Gopakumar-Vafa. Chin. Ann. Math. Ser. B 27, 219–242 (2006). https://doi.org/10.1007/s11401-006-0038-2

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  • Calabi-Yau threefold
  • Gromov-Witten invariants
  • Moduli of stable sheaves

2000 MR Subject Classification

  • 14D20
  • 14D21
  • 14J30
  • 14N35