Smooth toric Deligne-Mumford stacks

Barbara Fantechi (1) , Etienne Mann (1, 2) , Fabio Nironi (1)

1 SISSA / ISAS - Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies
2 I3M - Institut de Mathématiques et de Modélisation de Montpellier

We give a new definition of smooth toric DM stacks in the same spirit of toric varieties. We show that our definition is equivalent to the one of Borisov, Chen and Smith in terms of stacky fans. In particular, we give a geometric interpretation of the combinatorial data contained in a stacky fan. We also give a bottom up classification in terms of simplicial toric varieties and fiber products of root stacks.

Mots clés: Toric DM stacks; Stacky fans; Root stacks

Domaines: Géométrie algébrique [math.AG]

Barbara Fantechi, Etienne Mann, Fabio Nironi. Smooth toric Deligne-Mumford stacks. Journal für die reine und angewandte Mathematik, 2010, 648, pp.201-244. ⟨10.1515/CRELLE.2010.084⟩. ⟨hal-00166751v2⟩