Vol. 301, No. 2, 2019

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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
Authors
Atsushi Kanazawa
Department of Mathematics
Kyoto University
Japan
Siu-Cheong Lau
Department of Mathematics and Statistics
Boston University
United States