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

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References

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  • Iwanari, Isamu (2009). "The category of toric stacks". Compositio Mathematica. 145 (3): 718–746. arXiv:math/0610548. doi:10.1112/S0010437X09003911. S2CID 13941792.
  • Geraschenko, Anton; Satriano, Matthew (2015). "Toric stacks I: The theory of stacky fans". Transactions of the American Mathematical Society. 367 (2): 1033–1071. arXiv:1107.1906. doi:10.1090/S0002-9947-2014-06063-7. S2CID 5667546.
  • Iwanari, I. (2009). "Integral Chow Rings of Toric Stacks". International Mathematics Research Notices. arXiv:0705.3524. doi:10.1093/imrn/rnp110. S2CID 12047977.
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Toric variety

toric varieties Gordan's lemma Toric ideal Toric stack (roughly this is obtained by replacing the step of taking a GIT quotient by a quotient stack)

Stack (mathematics)

presheaf Stacks Project Toric stack Generalized space Alper, Jarod; Hall, Jack; Rydh, David (2020). "A Luna étale slice theorem for algebraic stacks". Annals

Algebraic stack

a stack Quotient stack Sheaf on an algebraic stack Toric stack Artin's criterion Pursuing Stacks Derived algebraic geometry A'Campo, Norbert; Ji, Lizhen;

Weighted projective space

quotient singularities. A weighted projective space is a Q-Fano variety and a toric variety. The weighted projective space P(a0,a1,...,an) is isomorphic to

Intraocular lens

for a toric IOL. Cataract surgery with implantation of a toric IOL is essentially the same as cataract surgery with a conventional IOL. Like toric contact

Andrew Kresch

Brauer groups and quotient stacks. American Journal of Mathematics, 123(4):761-777. Gromov-Witten invariants of a class of toric varieties (2000). Michigan

Hirzebruch surface

relative Proj—The Stacks project". stacks.math.columbia.edu. Retrieved 2020-05-23. Cox, David A.; Little, John B.; Schenck, Henry K. (2011). Toric varieties.

Indigo (Chris Brown album)

dancehall and bounce music, evident in tracks such as "You Like That", "Need a Stack", "Juice", "Wobble Up", "Back to Love" and "Lurkin'". Exclaim!'s Mike Juliano