The Gopakumar-Vafa formula for symplectic manifolds
| Autor: | Eleny-Nicoleta Ionel, Thomas H. Parker |
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| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Conjecture 010308 nuclear & particles physics 010102 general mathematics Zero (complex analysis) 01 natural sciences Mathematics - Algebraic Geometry High Energy Physics::Theory Mathematics::Algebraic Geometry Mathematics (miscellaneous) Integer Mathematics - Symplectic Geometry Genus (mathematics) 0103 physical sciences FOS: Mathematics Symplectic Geometry (math.SG) Mathematics::Differential Geometry 0101 mathematics Statistics Probability and Uncertainty Algebraic Geometry (math.AG) Mathematics::Symplectic Geometry Symplectic geometry Mathematics |
| Zdroj: | Annals of Mathematics. 187 |
| ISSN: | 0003-486X |
| DOI: | 10.4007/annals.2018.187.1.1 |
| Popis: | 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 formula 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. Comment: We have clarified the analytic setting by adding further details to Sections 4 and 5 and expanding the appendix, which now parts A and B. To appear in Annals of Mathematics |
| Databáze: | OpenAIRE |
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