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Abstract
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.
Received: 2009-01-21
Revised: 2009-09-19
Published Online: 2011-03-01
Published in Print: 2010-November
© Walter de Gruyter Berlin · New York 2010
