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arXiv · 1906.11749

$T$-equivariant disc potential and SYZ mirror construction

Yoosik Kim·Siu-Cheong Lau·Xiao Zheng
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Abstract

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}.

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Yoosik Kim, Siu-Cheong Lau, Xiao Zheng. 2019-06-27. $T$-equivariant disc potential and SYZ mirror construction. https://arxiv.org/abs/1906.11749

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