Geometric transitions and SYZ mirror symmetry

Atsushi Kanazawa and Siu-Cheong Lau

Vol. 301 (2019), No. 2, 489–517

DOI: 10.2140/pjm.2019.301.489

Abstract

We prove that generalized conifolds and orbifolded conifolds are mirror symmetric under the SYZ program with quantum corrections. Our work mathematically confirms the gauge-theoretic assertion of Aganagic–Karch–Lüst–Miemiec, and also provides a supportive evidence to Morrison’s conjecture that geometric transitions are reversed under mirror symmetry.

Keywords

SYZ, mirror symmetry, conifold transition, open Gromov-Witten invariants

Mathematical Subject Classification 2010

Primary: 14J33, 53D37

Milestones

Received: 12 March 2018

Revised: 1 November 2018

Accepted: 1 December 2018

Published: 24 October 2019