Toric Stacks Ii: Intrinsic Characterization of Toric Stacks
نویسندگان
چکیده
The purpose of this paper and its prequel is to introduce and develop a theory of toric stacks which encompasses and extends several notions of toric stacks defined in the literature, as well as classical toric varieties. While the focus of the prequel is on how to work with toric stacks, the focus of this paper is how to show a stack is toric. For toric varieties, a classical result says that a finite type scheme with an action of a dense open torus arises from a fan if and only if it is normal and separated. In the same spirit, the main result of this paper is that any Artin stack with an action of a dense open torus arises from a stacky fan under reasonable hypotheses.
منابع مشابه
Toric Stacks I: the Theory of Stacky Fans
The purpose of this paper and its sequel [GS11b] is to introduce and develop a theory of toric stacks which encompasses and extends the notions of toric stacks defined in [Laf02, BCS05, FMN10, Iwa09, Sat12, Tyo12], as well as classical toric varieties. In this paper, we define a toric stack as the stack quotient of a toric variety by a subgroup of its torus (we also define a generically stacky ...
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