Mirror of Atiyah flop in symplectic geometry and stability conditions

Atsushi Kanazawa Kyoto University Siu-Cheong Lau Boston University

Symplectic Geometry mathscidoc:1905.34001

Advances in Theoretical and Mathematical Physics
We carry out the SYZ program for the local Calabi--Yau manifolds of type $\widetilde{A}$ by developing an equivariant SYZ theory for the toric Calabi--Yau manifolds of infinite-type. Mirror geometry is shown to be expressed in terms of the Riemann theta functions and generating functions of open Gromov--Witten invariants, whose modular properties are found and studied in this article. Our work also provides a mathematical justification for a mirror symmetry assertion of the physicists Hollowood--Iqbal--Vafa.
Mirror symmetry, flop, stability conditions, special Lagrangians, SYZ
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@inproceedings{atsushimirror,
  title={Mirror of Atiyah flop in symplectic geometry and stability conditions},
  author={Atsushi Kanazawa, and Siu-Cheong Lau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190516210257038600346},
  booktitle={Advances in Theoretical and Mathematical Physics},
}
Atsushi Kanazawa, and Siu-Cheong Lau. Mirror of Atiyah flop in symplectic geometry and stability conditions. In Advances in Theoretical and Mathematical Physics. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190516210257038600346.
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