Gromov-Witten theory and Noether-Lefschetz theory for holomorphic-symplectic varieties

• Verfasst von: Oberdieck, Georg [VerfasserIn]
• Verfasst von: Song, Jieao [VerfasserIn]
• Titel: Gromov-Witten theory and Noether-Lefschetz theory for holomorphic-symplectic varieties
• Verf.angabe: Georg Oberdieck and with an appendix by Jieao Song
• E-Jahr: 2022
• Jahr: 04 April 2022
• Umfang: 46 S.
• Fussnoten: Gesehen am 12.12.2024
• Ang. zum Inhalt: Enthält außerdem: Appendix C. Geometry of a general singular Debarre–Voisin fourfold / by Jieao Song
• Titel Quelle: Enthalten in: Forum of mathematics. Sigma
• Ort Quelle: Cambridge : Cambridge Univ. Press, 2013
• Jahr Quelle: 2022
• Band/Heft Quelle: 10(2022), Artikel-ID e21, Seite 1-46
• ISSN Quelle: 2050-5094
• DOI: doi:10.1017/fms.2022.10
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: 14J28
• Sach-SW: 14J42
• Sach-SW: 14N35
• K10plus-PPN: 1912175401

Abstract

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.