Mirror of Atiyah flop in symplectic geometry and stability conditions

2017/06/09 by Yuwei Fan, Yu-Wei Fan, Fan, Yu-Wei +7 · 1 citation
Mathematics · #14J33 #53D37 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.AG #math.SG #msc:14J33 #msc:53D37

paper · pdf · doi:10.48550/arxiv.1706.02942

v2: 45 pages, 18 figures; revised exposition

openalex publication_date 2017/06/09 · arxiv created 2017/06/24 · arxiv updated 2017/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the mirror operation of the Atiyah flop in symplectic geometry. We formulate the operation for a symplectic manifold with a Lagrangian fibration. Furthermore we construct geometric stability conditions on the derived Fukaya category of the deformed conifold and study the action of the mirror Atiyah flop on these stability conditions.

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