Abstract
We develop a Floer theoretical gluing technique and apply it to deal with the most generic singular fiber 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 $\operatorname{Gr}(2,\mathbb{C}^n)$ and $\operatorname{OG}(1,\mathbb{C}^5)$ and derive their SYZ mirrors. It recovers the Lie theoretical mirrors constructed by Rietsch. It also gives an effective way to compute stable disks (with non-trivial obstructions) bounded by immersed Lagrangians.
Citation
Hansol Hong. Yoosik Kim. Siu-Cheong Lau. "Immersed two-spheres and SYZ with application to Grassmannians." J. Differential Geom. 125 (3) 427 - 507, November 2023. https://doi.org/10.4310/jdg/1701804149
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