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arXiv · 1701.00689

Twisted Polytope Sheaves and Coherent-Constructible Correspondence for Toric Varieties

Peng Zhou
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Abstract

Given a smooth projective toric variety $X_\Sigma$ of complex dimension $n$, Fang-Liu-Treumann-Zaslow \cite{FLTZ} showed that there is a quasi-embedding of the differential graded (dg) derived category of coherent sheaves $Coh(X_\Sigma)$ into the dg derived category of constructible sheaves on a torus $Sh(T^n, \Lambda_\Sigma)$. Recently, Kuwagaki \cite{Ku2} proved that the quasi-embedding is a quasi-equivalence, and generalized the result to toric stacks. Here we give a different proof in the smooth projective case, using non-characteristic deformation of sheaves to find twisted polytope sheaves that co-represent the stalk functors.

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Peng Zhou. 2017-01-03. Twisted Polytope Sheaves and Coherent-Constructible Correspondence for Toric Varieties. https://arxiv.org/abs/1701.00689

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