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Mirror theorem for elliptic quasimap invariants

Bumsig Kim and Hyenho Lho

Geometry & Topology 22 (2018) 1459–1481
Abstract

We propose and prove a mirror theorem for the elliptic quasimap invariants of smooth Calabi–Yau complete intersections in projective spaces. This theorem, combined with the wall-crossing formula of Ciocan-Fontanine and Kim, implies mirror theorems of Zinger and Popa for the elliptic Gromov–Witten invariants of those varieties. This paper and the wall-crossing formula provide a unified framework for the mirror theory of rational and elliptic Gromov–Witten invariants.

Keywords
mirror theorem, elliptic quasimap invariants, elliptic Gromov-Witten invariants
Mathematical Subject Classification 2010
Primary: 14N35
Secondary: 14D23
References
Publication
Received: 1 May 2016
Revised: 28 March 2017
Accepted: 6 June 2017
Published: 16 March 2018
Proposed: Richard Thomas
Seconded: Jim Bryan, Dan Abramovich
Authors
Bumsig Kim
School of Mathematics
Korea Institute for Advanced Study
Seoul
South Korea
Hyenho Lho
Department of Mathematics
ETH
Zürich
Switzerland