Homological mirror symmetry at large volume

Benjamin Gammage, Vivek Shende

Publikation: Working paperForskning

Abstrakt

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.
OriginalsprogEngelsk
UdgiverarXiv.org
Antal sider31
StatusUdgivet - 22. apr. 2021

Bibliografisk note

31 pages

Emneord

  • math.SG
  • math.AG

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