The Coherent–Constructible Correspondence for Toric Deligne–Mumford Stacks.

We extend our previous work [8] on coherent–constructible correspondence for toric varieties to toric Deligne–Mumford (DM) stacks. Following Borisov et al. [3], a toric DM stack is described by a “stacky fan” Σ=(N,Σ,β), where N is a finitely generated abelian group and Σ is a simplicial fan in . From Σ, we define a conical Lagrangian ΛΣ inside the cotangent of the dual vector space of , such that torus-equivariant, coherent sheaves on are equivalent to constructible sheaves on with singular support in ΛΣ. The microlocalization theorem of Nadler and the last author [18, 19] provides an algebro-geometrical description of the Fukaya category of a cotangent bundle in terms of constructible sheaves on the base . This allows us to interpret the main theorem stated earlier as an equivariant version of homological mirror symmetry for toric DM stacks. [ABSTRACT FROM AUTHOR]