Smooth toric Deligne-Mumford stacks

被引：79
|
作者：
Fantechi, Barbara [1 ]
Mann, Etienne [2 ]
Nironi, Fabio [3 ]
机构：
[1] SISSA, I-34014 Trieste, Italy
[2] Univ Montpellier 2, Inst Math & Modelisat Montpellier, F-34095 Montpellier, France
[3] Columbia Univ, Dept Math, New York, NY 10027 USA
来源：
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK | 2010年 / 648卷
关键词：
D O I：
10.1515/CRELLE.2010.084
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We give a geometric definition of smooth toric Deligne-Mumford stacks using the action of a "torus". 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.
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页码：201 / 244
页数：44
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