Gromov-Witten invariants of Calabi-Yau fibrations

Abstract

We study the quasimap invariants of elliptic and K3 fibrations. Oberdieck and Pixton conjectured that the Gromov-Witten potentials of elliptic fibrations are quasi-modular forms. Analogously, we propose similar conjecture for the quasimap potentials of elliptic fibrations. We also conjecture some finite generation properties of quasimap potentials of K3 fibrations. Via wall-crossing conjecture, this will imply some quasi-modularity of the Gromov-Witten potentials of K3 fibrations. We provide some evidences for our conjectures through several examples. The method here can be further generalized to arbitrary n-dimensional Calabi-Yau fibrations.

arXiv comment35 pages

References in corpus (6)

• Moduli stacks of stable toric quasimaps
• Mirror Theorem for Elliptic Quasimap Invariants
• Structure of Higher Genus Gromov-Witten Invariants of Quintic 3-folds
• Polynomial structure of Gromov-Witten potential of quintic $3$-folds via NMSP
• Crepant resolution and the holomorphic anomaly equation for C^3/Z_3
• Equivariant holomorphic anomaly equation