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 action of the torus on itself extends to the whole variety. Some authors also require it to be normal. Toric varieties form an important and rich class of examples in algebraic geometry, which often provide a testing ground for theorems. The geometry of a toric variety is fully determined by the combinatorics of its associated fan, which often makes computations far more tractable. For a certain special, but still quite general class of toric varieties, this information is also encoded in a polytope, which creates a powerful connection of the subject with convex geometry. Familiar examples of toric varieties are affine space, projective spaces, products of projective spaces and bundles over projective space.
In algebraic geometry, a toricvariety or torus embedding is an algebraic variety containing an algebraic torus as an open dense subset, such that the...
construction by David A. Cox in 1995 for toricvarieties. Cox, David A. (1995), "The homogeneous coordinate ring of a toricvariety", J. Algebraic Geom., 4 (1): 17–50...
associated toric fan. This makes toricvarieties a particularly attractive test case for many constructions in complex geometry. Examples of toricvarieties include...
(1993), Introduction to toricvarieties, Princeton University Press, ISBN 978-0-691-00049-7, a remark describes a complete toricvariety that has no non-trivial...
Toric manifold Toric orbifold Toric section ToricvarietyToric lens, a type of optical lens Torić, a village in Bosnia and Herzegovina Toric Robinson (born...
classes of toricvarieties, the Riemann–Roch theorem as well as Fourier analysis have been used for this purpose. If X is the toricvariety corresponding...
projective algebraic variety defined by a toric ideal or a homogeneous toric ideal is an affine or projective toricvariety, possibly non-normal. Let K {\displaystyle...
In mathematics, a toric manifold is a topological analogue of toricvariety in algebraic geometry. It is an even-dimensional manifold with an effective...
a toric stack is a stacky generalization of a toricvariety. More precisely, a toric stack is obtained by replacing in the construction of a toric variety...
featured in the theory of toricvarieties, where they correspond to polarized projective toricvarieties. For instance, the toricvariety corresponding to a...
In mathematics, a hypertoric variety or toric hyperkähler variety is a quaternionic analog of a toricvariety constructed by applying the hyper-Kähler...
quotient singularities. A weighted projective space is a Q-Fano variety and a toricvariety. The weighted projective space P(a0,a1,...,an) is isomorphic...
orbifold). A normal algebraic variety with a torus acting on it in such a way that there is a dense orbit is called a toricvariety (for example, orbit closures...
of scalars of F1‑varieties to Z are toric. Whilst other approaches to F1‑geometry admit wider classes of examples, toricvarieties appear to lie at the...
"toric manifolds". However, the term "quasitoric manifold" was eventually adopted to avoid confusion with the class of compact smooth toricvarieties,...
an open embedding of algebraic varieties that locally looks like the embedding of the open torus into a toricvariety. The notion was introduced by Mumford...
Singularities of toricvarieties give examples of high-dimensional singularities that are easy to resolve explicitly. A toricvariety is defined by a fan...
compactification of the subvariety is defined as a closure of it in a toricvariety of the original torus. The concept of a tropical compactification arises...
an important role in the theory of toricvarieties, where it corresponds to projective normality of the toricvariety determined by P. Normal polytopes...
and (affine or projective) toricvarieties. There is also a notion of real spherical varieties. A projective spherical variety is a Mori dream space. Spherical...
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...
geometry. torus embedding An old term for a toricvarietytoricvariety A toricvariety is a normal variety with the action of a torus such that the torus...
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