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

2021/02/23 by Oberdieck, Georg · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2102.11622

Abstract

We use Noether-Lefschetz theory to study the reduced Gromov--Witten invariants of a holomorphic-symplectic variety of 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 HLS divisors on the moduli space of Debarre-Voisin fourfolds.

Cited by

• Hilbert squares of genus 16 K3 surfaces
• Peskine sixfolds and Debarre-Voisin fourfolds with associated cubic fourfolds

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