In algebraic geometry, a toric variety or torus embedding is an algebraic variety containing an algebraic torus as an open dense subset, such that the...

associated toric fan. This makes toric varieties a particularly attractive test case for many constructions in complex geometry. Examples of toric varieties include...

All the theory above generalizes to arbitrary toric varieties, including the construction of the variety as a quotient and by coordinate charts, as well...

(1993), Introduction to toric varieties, Princeton University Press, ISBN 978-0-691-00049-7, a remark describes a complete toric variety that has no non-trivial...

construction by David A. Cox in 1995 for toric varieties. Cox, David A. (1995), "The homogeneous coordinate ring of a toric variety", J. Algebraic Geom., 4 (1): 17–50...

classes of toric varieties, the Riemann–Roch theorem as well as Fourier analysis have been used for this purpose. If X is the toric variety corresponding...

Toric manifold Toric orbifold Toric section Toric variety Toric lens, a type of optical lens Torić, a village in Bosnia and Herzegovina Toric Robinson (born...

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...

featured in the theory of toric varieties, where they correspond to polarized projective toric varieties. For instance, the toric variety corresponding to a...

In mathematics, a hypertoric variety or toric hyperkähler variety is a quaternionic analog of a toric variety constructed by applying the hyper-Kähler...

In mathematics, a toric manifold is a topological analogue of toric variety in algebraic geometry. It is an even-dimensional manifold with an effective...

computationally determine when a given toric surface is K-stable. An example of a K-unstable manifold is given by the toric surface F 1 = Bl 0 ⁡ C P 2 {\displaystyle...

convex polyhedral cone is finitely generated. An affine toric variety is an algebraic variety (this follows from the fact that the prime spectrum of the...

projective algebraic variety defined by a toric ideal or a homogeneous toric ideal is an affine or projective toric variety, possibly non-normal. Let K {\displaystyle...

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...

an open embedding of algebraic varieties that locally looks like the embedding of the open torus into a toric variety. The notion was introduced by Mumford...

original URL status unknown (link) Quiver representations in toric geometry Projective toric varieties as fine moduli spaces of quiver representations Wikimedia...

"toric manifolds". However, the term "quasitoric manifold" was eventually adopted to avoid confusion with the class of compact smooth toric varieties,...

of scalars of F1‑varieties to Z are toric. Whilst other approaches to F1‑geometry admit wider classes of examples, toric varieties appear to lie at the...

Singularities of toric varieties give examples of high-dimensional singularities that are easy to resolve explicitly. A toric variety is defined by a fan...

generalization of the notion of the Newton polytope of a projective toric variety. It was introduced (in passing) by Andrei Okounkov in his papers in...

projective plane Sphere Spiric section Surface (topology) Toric lens Toric section Toric variety Toroid Toroidal and poloidal Torus-based cryptography Torus...

orbifold). A normal algebraic variety with a torus acting on it in such a way that there is a dense orbit is called a toric variety (for example, orbit closures...

compactification of the subvariety is defined as a closure of it in a toric variety of the original torus. The concept of a tropical compactification arises...

2020). "Tory Lanez Denies Megan Thee Stallion's Account of Being Shot in a Highly Defensive Surprise Album". Variety. Retrieved October 1, 2020. "Tory Lanez...

computer-based algebraic geometry (such as Gröbner basis), Torelli sets and toric varieties, and history of mathematics. He is also known for several textbooks...

"toric" is a connection of the toric h-vector with the intersection cohomology of a certain projective toric variety X whenever P is the boundary complex...

theory Symbolic method of invariant theory Geometric invariant theory Toric variety Deformation theory Singular point, non-singular Singularity theory Newton...

an important role in the theory of toric varieties, where it corresponds to projective normality of the toric variety determined by P. Normal polytopes...

geometry. torus embedding An old term for a toric variety toric variety A toric variety is a normal variety with the action of a torus such that the torus...