The Gopakumar-Vafa formula for symplectic manifolds

• 成果类型: Article
• 署名作者: Ionel, Eleny-Nicoleta; Parker, Thomas H.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2018.187.1.1
• 发表日期: 2018
• 页码: 1-64
• 关键词: gromov-witten invariants; kahler surfaces; CURVES; THEOREM; INTEGRALS

摘要

The Gopakumar-Vafa conjecture predicts that the Gromov-Witten invariants of a Calabi-Yau 3-fold can be canonically expressed in terms of integer invariants called BPS numbers. Using the methods of symplectic Gromov-Witten theory, we prove that the Gopakumar-Vafa conjecture holds for any symplectic Calabi-Yau 6-manifold, and hence for Calabi-Yau 3-folds. The results extend to all symplectic 6-manifolds and to the genus zero GW invariants of semipositive manifolds.