Immersed two-spheres and SYZ with applications to Grassmannians

Hansol Hong Yonsei University Yoosik Kim Pusan National University Siu-Cheong Lau Boston University

Differential Geometry mathscidoc:2107.10001

JDG, 2021.7
We develop a Floer theoretical gluing technique and apply it to deal with the most generic singular ber in the SYZ program, namely the product of a torus with the immersed two-sphere with a single nodal self-intersection. As an application, we construct immersed Lagrangians in Gr(2;Cn) and OG(1;C5) and derive their SYZ mirrors. It recovers the Lie theoretical mirrors constructed by Rietsch. It also gives an e ective way to compute stable disks (with non-trivial obstructions) bounded by immersed Lagrangians.
SYZ, mirror symmetry, Lagrangian Floer theory, immersed sphere, Grassmannian
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@inproceedings{hansol2021immersed,
  title={Immersed two-spheres and SYZ with applications to Grassmannians},
  author={Hansol Hong, Yoosik Kim, and Siu-Cheong Lau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210714012658903534851},
  booktitle={JDG},
  year={2021},
}
Hansol Hong, Yoosik Kim, and Siu-Cheong Lau. Immersed two-spheres and SYZ with applications to Grassmannians. 2021. In JDG. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210714012658903534851.
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