Gromov-Witten theory and Noether-Lefschetz theory for holomorphic-symplectic varieties
We use Noether-Lefschetz theory to study the reduced Gromov-Witten invariants of a holomorphic-symplectic variety of - - - - K3[n]K3[n]K3^{[n]} - - - -type. This yields strong evidence for a new conjectural formula that expresses Gromov-Witten invariants of this geometry for arbitrary classes...
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| Hauptverfasser: | , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
04 April 2022
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| In: |
Forum of mathematics. Sigma
Year: 2022, Jahrgang: 10, Pages: 1-46 |
| ISSN: | 2050-5094 |
| DOI: | 10.1017/fms.2022.10 |
| Online-Zugang: | Verlag, kostenfrei, Volltext: https://doi.org/10.1017/fms.2022.10 Verlag, kostenfrei, Volltext: https://www.cambridge.org/core/journals/forum-of-mathematics-sigma/article/gromovwitten-theory-and-noetherlefschetz-theory-for-holomorphicsymplectic-varieties/254A0340D7FE477467F5FF74CC865977 
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| Verfasserangaben: | Georg Oberdieck and with an appendix by Jieao Song |
MARC
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| 245 | 1 | 0 | |a Gromov-Witten theory and Noether-Lefschetz theory for holomorphic-symplectic varieties |c Georg Oberdieck and with an appendix by Jieao Song |
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| 505 | 8 | 0 | |t Enthält außerdem: Appendix C. Geometry of a general singular Debarre–Voisin fourfold |r by Jieao Song |
| 520 | |a We use Noether-Lefschetz theory to study the reduced Gromov-Witten invariants of a holomorphic-symplectic variety of - - - - K3[n]K3[n]K3^{[n]} - - - -type. This yields strong evidence for a new conjectural formula that expresses Gromov-Witten invariants of this geometry for arbitrary classes in terms of primitive classes. The formula generalizes an earlier conjecture by Pandharipande and the author for K3 surfaces. Using Gromov-Witten techniques, we also determine the generating series of Noether-Lefschetz numbers of a general pencil of Debarre-Voisin varieties. This reproves and extends a result of Debarre, Han, O’Grady and Voisin on Hassett-Looijenga-Shah (HLS) divisors on the moduli space of Debarre-Voisin fourfolds. | ||
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