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arXiv · 1805.11738

Immersed two-spheres and SYZ with Application to Grassmannians

Hansol Hong·Yoosik Kim·Siu-Cheong Lau
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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 $\mathrm{Gr}(2,\mathbb{C}^n)$ and $\mathrm{OG}(1,\mathbb{C}^5)$ 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.

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Hansol Hong, Yoosik Kim, Siu-Cheong Lau. 2018-05-29. Immersed two-spheres and SYZ with Application to Grassmannians. https://arxiv.org/abs/1805.11738

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