The Coherent-Constructible Correspondence for Toric Deligne-Mumford Stacks

Abstract

We extend our previous work arXiv:1007.0053 on coherent-constructible correspondence for toric varieties to include toric Deligne-Mumford (DM) stacks. Following Borisov-Chen-Smith, a toric DM stack $\cX_\bSi$ is described by a "stacky fan" $\bSi=(N,\Si,β)$, where $N$ is a finitely generated abelian group and $\Si$ is a simplicial fan in $N_\bR=N\otimes_{\bZ}\bR$. From $\bSi$ we define a conical Lagrangian $Λ_\bSi$ inside the cotangent $T^*M_\bR$ of the dual vector space $M_\bR$ of $N_\bR$, such that torus-equivariant, coherent sheaves on $\cX_\bSi$ are equivalent to constructible sheaves on $M_\bR$ with singular support in $\LbS$.

30 pages, 2 figures

References in corpus (3)

• Log Crepant Birational Maps and Derived Categories
• Smooth toric DM stacks
• Tropical coamoeba and torus-equivariant homological mirror symmetry for the projective space

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• Exact Lefschetz fibrations associated with dimer models
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• Mirror Symmetry in dimension one and Fourier-Mukai equivalences
• The Coherent-Constructible Correspondence and Fourier-Mukai Transforms