- Author(s): Geraschenko, Anton Igorevich
- Advisor(s): Serganova, Vera V
- et al.
The first purpose of this dissertation is to introduce and develop a theory of toric stacks which encompasses and extends the notions of toric stacks defined by Lafforgue, Borisov-Chen-Smith, Fantechi-Mann-Nironi, Iwanari, and Satriano, as well as classical toric varieties. In addition to introducing a broader class of smooth toric stacks, the definition we introduce allows singularities.
The second purpose is to characterize toric stacks in a "bottom up" fashion, similar to the treatment of smooth toric Deligne-Mumford stacks by Fantechi-Mann-Nironi and the characterization of toric varieties as "abstract toric schemes" which are reduced, separated, and normal.