Gromov-Witten theory and Noether-Lefschetz theory for holomorphic-symplectic varieties - Oberdieck, Georg; Song, Jieao (Forum of mathematics. Sigma, 2022)
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.
Gesehen am 12.12.2024