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arXiv · 2104.11129

Homological mirror symmetry at large volume

Benjamin Gammage·Vivek Shende
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Abstract

A typical large complex-structure limit for mirror symmetry consists of toric varieties glued to each other along their toric boundaries. Here we construct the mirror large volume limit space as a Weinstein symplectic manifold. We prove homological mirror symmetry: the category of coherent sheaves on the first space is equivalent to the Fukaya category of the second. Our equivalence intertwines the Viterbo restriction maps for a generalized pair-of-pants cover of the symplectic manifold with the restriction of coherent sheaves for a certain affine cover of the algebraic variety. We deduce a posteriori a local-to-global principle conjectured by Seidel -- certain diagrams of Viterbo restrictions are cartesian -- by passing Zariski descent through our mirror symmetry result.

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Benjamin Gammage, Vivek Shende. 2021-04-22. Homological mirror symmetry at large volume. https://doi.org/10.2140/tunis.2023.5.31

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