Advances in Theoretical and Mathematical Physics

Volume 22 (2018)

Number 5

Mirror of Atiyah flop in symplectic geometry and stability conditions

Pages: 1149 – 1207

DOI: https://dx.doi.org/10.4310/ATMP.2018.v22.n5.a2

Authors

Yu-Wei Fan (Department of Mathematics, Harvard University, Cambridge, Massachusetts, U.S.A.)

Hansol Hong (Department of Mathematics, Yonsei University, Seoul, Korea)

Siu-Cheong Lau (Department of Mathematics and Statistics, Boston University, Boston, Massachusetts, U.S.A.)

Shing-Tung Yau (Department of Mathematics, Harvard University, Cambridge, Massachusetts, U.S.A.)

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

Published 2 May 2019