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Smooth toric Deligne-Mumford stacks
-
Barbara Fantechi
,
Etienne Mann
Published/Copyright:
March 1, 2011
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
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Articles in the same Issue
- In memoriam Ernst Steinitz (1871–1928)
- Kuga-Satake abelian varieties of K3 surfaces in mixed characteristic
- Knotted holomorphic discs in
- Smoothness of Lipschitz minimal intrinsic graphs in Heisenberg groups , n > 1
- Big projective modules over noetherian semilocal rings
- On Néron-Raynaud class groups of tori and the capitulation problem
- Weil restriction and support varieties
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