Twisted Polytope Sheaves and Coherent-Constructible Correspondence for Toric Varieties

2017/01/03 by Zhou, Peng · 1 citation
#Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1701.00689

Abstract

Given a smooth projective toric variety X_Σ of complex dimension n, Fang-Liu-Treumann-Zaslow \citeFLTZ showed that there is a quasi-embedding of the differential graded (dg) derived category of coherent sheaves Coh(X_Σ) into the dg derived category of constructible sheaves on a torus Sh(Tⁿ, Λ_Σ). Recently, Kuwagaki \citeKu2 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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