Gromov-Witten theory and Noether-Lefschetz theory for holomorphic-symplectic varieties
Abstract
We use Noether-Lefschetz theory to study the reduced Gromov--Witten invariants of a holomorphic-symplectic variety of -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 HLS divisors on the moduli space of Debarre-Voisin fourfolds.
Keywords
Cite
@article{arxiv.2102.11622,
title = {Gromov-Witten theory and Noether-Lefschetz theory for holomorphic-symplectic varieties},
author = {Georg Oberdieck},
journal= {arXiv preprint arXiv:2102.11622},
year = {2022}
}
Comments
46 pages, minor changes, more details on proof of Corollary 1. v3: added appendix by J. Song about the geometry of a general singular Debarre-Voisin 4-fold; expanded discussion at a few places; typos fixed