The coherent-constructible correspondence for toric deligne-mumford stacks

Bohan Fang*, Chiu Chu Melissa Liu, David Treumann, Eric Zaslow

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


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 χΣ 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 NR = N Z R. From Σ, we define a conical Lagrangian ΛΣ inside the cotangent T*MRof the dual vector space MRof N R, such that torus-equivariant, coherent sheaves on χΣ are equivalent to constructible sheaves on MR 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 T*MR in terms of constructible sheaves on the base MR. This allows us to interpret the main theorem stated earlier as an equivariant version of homological mirror symmetry for toric DM stacks.

Original languageEnglish (US)
Pages (from-to)914-954
Number of pages41
JournalInternational Mathematics Research Notices
Issue number4
StatePublished - Nov 2014

ASJC Scopus subject areas

  • Mathematics(all)


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