# Toric stack

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In [algebraic geometry](/source/algebraic_geometry), a '''toric stack''' is a [stacky](/source/stack_(mathematics)) generalization of a [toric variety](/source/toric_variety). More precisely, a toric stack is obtained by replacing in the construction of a toric variety a step of taking [GIT quotient](/source/GIT_quotient)s with that of taking [quotient stack](/source/quotient_stack)s. 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](/source/Stanley%E2%80%93Reisner_ring)

== References ==
*{{cite journal |title=The category of toric stacks |year=2009|doi=10.1112/S0010437X09003911|arxiv=math/0610548|last1=Iwanari|first1=Isamu|s2cid=13941792|journal=Compositio Mathematica|volume=145|issue=3|pages=718–746}}
*{{cite journal |first1=Anton |last1=Geraschenko |first2=Matthew |last2=Satriano |doi=10.1090/S0002-9947-2014-06063-7|title=Toric stacks I: The theory of stacky fans|year=2015|s2cid=5667546|journal=Transactions of the American Mathematical Society|volume=367|issue=2|pages=1033–1071|arxiv=1107.1906}}
*{{cite journal |doi=10.1093/imrn/rnp110|title=Integral Chow Rings of Toric Stacks|year=2009|last1=Iwanari|first1=I.|s2cid=12047977|journal=International Mathematics Research Notices|arxiv=0705.3524}}

Category:Stacks (mathematics)
{{algebraic-geometry-stub}}

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