Mirror Theorem for Elliptic Quasimap Invariants
Bumsig Kim, Hyenho Lho
TL;DR
This paper establishes a mirror theorem for elliptic quasimap invariants of Calabi-Yau complete intersections, linking it with existing Gromov-Witten theories and providing a unified framework for rational and elliptic cases.
Contribution
It proves a new mirror theorem for elliptic quasimap invariants and integrates it with wall-crossing formulas to unify rational and elliptic Gromov-Witten invariants.
Findings
Proved mirror theorem for elliptic quasimap invariants.
Connected elliptic quasimap invariants with Gromov-Witten invariants.
Unified framework for rational and elliptic Gromov-Witten theories.
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.
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