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 journalArticle

7 Citations (Scopus)

Abstract

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
Volume2014
Issue number4
DOIs
StatePublished - Nov 1 2014

Fingerprint

Constructible
Correspondence
Sheaves
Equivariant
Cotangent
Mirror Symmetry
Coherent Sheaf
Cotangent Bundle
Toric Varieties
Finitely Generated Group
Theorem
Abelian group
Vector space
Torus
Fan

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Fang, Bohan ; Liu, Chiu Chu Melissa ; Treumann, David ; Zaslow, Eric. / The coherent-constructible correspondence for toric deligne-mumford stacks. In: International Mathematics Research Notices. 2014 ; Vol. 2014, No. 4. pp. 914-954.
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The coherent-constructible correspondence for toric deligne-mumford stacks. / Fang, Bohan; Liu, Chiu Chu Melissa; Treumann, David; Zaslow, Eric.

In: International Mathematics Research Notices, Vol. 2014, No. 4, 01.11.2014, p. 914-954.

Research output: Contribution to journalArticle

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