$T$-equivariant disc potential and SYZ mirror construction
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arXiv
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| Format: | Preprint |
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2019
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| _version_ | 1866910912116424704 |
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| author | Kim, Yoosik Lau, Siu-Cheong Zheng, Xiao |
| author_facet | Kim, Yoosik Lau, Siu-Cheong Zheng, Xiao |
| contents | We develop a $G$-equivariant Lagrangian Floer theory and obtain a curved $A_\infty$ algebra, and in particular a $G$-equivariant disc potential. We construct a Morse model, which counts pearly trees in the Borel construction $L_G$. When applied to a smooth moment map fiber of a semi-Fano toric manifold, our construction recovers the $T$-equivariant toric Landau-Ginzburg mirror of Givental. We also study the $\bS^1$-equivariant Floer theory of a typical singular SYZ fiber (i.e. a pinched torus) and compute its $\bS^1$-equivariant disc potential via the gluing technique developed in \cite{CHL18,HKL}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1906_11749 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | $T$-equivariant disc potential and SYZ mirror construction Kim, Yoosik Lau, Siu-Cheong Zheng, Xiao Symplectic Geometry Algebraic Geometry 53D37, 14J33 We develop a $G$-equivariant Lagrangian Floer theory and obtain a curved $A_\infty$ algebra, and in particular a $G$-equivariant disc potential. We construct a Morse model, which counts pearly trees in the Borel construction $L_G$. When applied to a smooth moment map fiber of a semi-Fano toric manifold, our construction recovers the $T$-equivariant toric Landau-Ginzburg mirror of Givental. We also study the $\bS^1$-equivariant Floer theory of a typical singular SYZ fiber (i.e. a pinched torus) and compute its $\bS^1$-equivariant disc potential via the gluing technique developed in \cite{CHL18,HKL}. |
| title | $T$-equivariant disc potential and SYZ mirror construction |
| topic | Symplectic Geometry Algebraic Geometry 53D37, 14J33 |
| url | https://arxiv.org/abs/1906.11749 |