Toric stack explained

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

• The category of toric stacks . 2009. 10.1112/S0010437X09003911. math/0610548. Iwanari. Isamu. 13941792. Compositio Mathematica. 145. 3. 718–746.
• Anton . Geraschenko . Matthew . Satriano . 10.1090/S0002-9947-2014-06063-7. Toric stacks I: The theory of stacky fans. 2015. 5667546. Transactions of the American Mathematical Society. 367. 2. 1033–1071. 1107.1906.
• 10.1093/imrn/rnp110. Integral Chow Rings of Toric Stacks. 2009. Iwanari. I.. 12047977. International Mathematics Research Notices. 0705.3524.