The Coherent-Constructible Correspondence for Toric Deligne-Mumford Stacks

Details The Coherent-Constructible Correspondence for Toric Deligne-Mumford Stacks The Coherent-Constructible Correspondence for Toric Deligne-Mumford Stacks

2009-11-24

arxiv.org/abs/0911.4711v2

Mathematics

Algebraic Geometry

30 pages, 2 figures

Scientific paper

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" $\bSi=(N,\Si,\beta)$, 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 $\Lambda_\bSi$ 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 $\LbS$.

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