Geometric transitions and SYZ mirror symmetry
Atsushi Kanazawa, Siu-Cheong Lau
TL;DR
This paper proves that certain geometric structures called punctured generalized conifolds and orbifolded conifolds are mirror symmetric under the SYZ program with quantum corrections, confirming predictions and conjectures in mirror symmetry.
Contribution
It provides a rigorous mathematical proof of mirror symmetry for these geometric transitions, supporting gauge-theoretic predictions and Morrison's conjecture.
Findings
Confirmed mirror symmetry for punctured generalized conifolds and orbifolded conifolds.
Validated gauge-theoretic predictions by Aganagic et al.
Supported Morrison's conjecture on the reversal of geometric transitions under mirror symmetry.
Abstract
We prove that the punctured generalized conifolds and punctured orbifolded conifolds are mirror symmetric under the SYZ program with quantum corrections. This mathematically confirms the gauge-theoretic prediction by Aganagic-Karch-L\"ust-Miemiec, and also provides a supportive evidence to Morrison's conjecture that geometric transitions are reversed under mirror symmetry.
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