The category of toric stacks

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21 Citations (Scopus)

Abstract

In this paper, we show that there is an equivalence between the 2-category of smooth Deligne-Mumford stacks with torus embeddings and actions and the 1-category of stacky fans. To this end, we prove two main results. The first is related to a combinatorial aspect of the 2-category of toric algebraic stacks defined by I. Iwanari [Logarithmic geometry, minimal free resolutions and toric algebraic stacks, Preprint (2007)]; we establish an equivalence between the 2-category of toric algebraic stacks and the 1-category of stacky fans. The second result provides a geometric characterization of toric algebraic stacks. Logarithmic geometry in the sense of Fontaine-Illusie plays a central role in obtaining our results.

Original languageEnglish
Pages (from-to)718-746
Number of pages29
JournalCompositio Mathematica
Volume145
Issue number3
DOIs
Publication statusPublished - 2009 May

Keywords

  • algebraic stacks
  • logarithmic geometry
  • toric geometry

ASJC Scopus subject areas

  • Algebra and Number Theory

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