John Nolan
The Ohio State University
Title
Functorial Classification of Toric Stacks
Abstract
Toric varieties and their stack-theoretic generalizations are common objects of study in algebraic geometry and mirror symmetry. It is well-known that toric varieties are classified by combinatorial objects known as "fans," and conventional wisdom tells us that toric stacks (whatever they are) should also be classified by more general "stacky fans." In 2011, Geraschenko and Satriano (henceforth GS) proposed a definition of stacky fans, giving a combinatorial construction of a large class of toric Artin stacks. Gillam and Molcho later observed that the GS construction is not essentially surjective, i.e. there exist objects which deserve to be called "toric stacks" but do not arise via the GS construction. Our goal in this talk is to introduce a new, more general notion of "stacky fan" and explain how to construct an equivalence between our 2-category of stacky fans and a suitable 2-category of toric stacks. (We will also include a brief review of stack theory for the uninitiated.)
