Gromov-Witten classes of K3 surfaces

Abstract

We study the cycle-valued reduced Gromov-Witten theory of a nonsingular projective K3 surface. For primitive curve classes, we prove that the correspondence induced by the reduced virtual fundamental class respects the tautological rings. Our proof uses monodromy over the moduli space of K3 surfaces, degeneration formulae and virtual localization. As a consequence of the monodromy argument, we verify an invariance property for Gromov-Witten invariants of K3 surfaces in primitive curve class conjectured by Oberdieck-Pandharipande.

arXiv comment17 pages, comments welcome

References in corpus (5)

• Reduced classes and curve counting on surfaces I: theory
• Holomorphic anomaly equations and the Igusa cusp form conjecture
• Gromov-Witten theory of target curves and the tautological ring
• Relations in the tautological ring of the moduli space of K3 surfaces
• Cohomological field theories with non-tautological classes

Cited by in corpus (1)

• Multiple cover formulas for K3 geometries, wall-crossing, and Quot schemes