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Geometric transitions and SYZ 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.Comment: v3: one compact example added. 25 pages, 12 figure

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