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arXiv · 1904.10315

Gromov-Witten invariants of Calabi-Yau fibrations

Hyenho Lho
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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.

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Hyenho Lho. 2019-04-21. Gromov-Witten invariants of Calabi-Yau fibrations. https://arxiv.org/abs/1904.10315

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