Mirror Theorem for Elliptic Quasimap Invariants

Abstract

We propose and prove a mirror theorem for the elliptic quasimap invariants for smooth Calabi-Yau complete intersections in projective spaces. The theorem combined with the wall-crossing formula appeared in paper (arXiv:1308.6377) implies mirror theorems of Zinger and Popa for the elliptic Gromov-Witten invariants for those varieties. This paper and the wall-crossing formula provide a unified framework for the mirror theory of rational and elliptic Gromov-Witten invariants.

Theorem 2.6 strengthened for the toric setup

Cited by in corpus (17)

• Quasimap Wall-crossings and Mirror Symmetry
• Virtual cycles of stable (quasi)-maps with fields
• BCOV's Feynman rule of quintic $3$-folds
• Towards a quantum Lefschetz hyperplane theorem in all genera
• The Genus-One Global Mirror Theorem for the Quintic Threefold
• Crepant resolution and the holomorphic anomaly equation for C^3/Z_3
• Quasimap wall-crossing for GIT quotients
• Genus one GW invariants of quintic threefolds via MSP localization
• Invariants of stable quasimaps with fields
• Quantum Lefschetz without curves
• Equivariant holomorphic anomaly equation
• Genus one stable quasimap invariants for projective complete intersections
• Gromov-Witten invariants of Calabi-Yau fibrations
• Variations on the theme of quantum Lefschetz
• Crepant resolution conjecture for ${\mathbb{C}}^5/{\mathbb{Z}}_5$
• $K$-theoretic quasimap wall-crossing
• Vanishing of Gromov-Witten invariants of product of P1