Smooth toric DM stacks

Understand

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.