Toric stack

In algebraic geometry, a toric stack is a stacky generalization of a toric variety. More precisely, a toric stack is obtained by replacing in the construction of a toric variety a step of taking GIT quotients with that of taking quotient stacks. Consequently, a toric variety is a coarse approximation of a toric stack. A toric orbifold is an example of a toric stack.

See also

• Stanley–Reisner ring

References

• Iwanari, Isamu (2009). "The category of toric stacks". Compositio Mathematica 145 (3): 718–746. doi:10.1112/S0010437X09003911. 
• Geraschenko, Anton; Satriano, Matthew (2015). "Toric stacks I: The theory of stacky fans". Transactions of the American Mathematical Society 367 (2): 1033–1071. doi:10.1090/S0002-9947-2014-06063-7. 
• Iwanari, I. (2009). "Integral Chow Rings of Toric Stacks". International Mathematics Research Notices. doi:10.1093/imrn/rnp110.