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...
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Complex geometry (section Toric varieties)
associated toric fan. This makes toric varieties a particularly attractive test case for many constructions in complex geometry. Examples of toric varieties include...
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Hirzebruch surface (section Toric variety)
All the theory above generalizes to arbitrary toric varieties, including the construction of the variety as a quotient and by coordinate charts, as well...
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(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...
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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...
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Ehrhart polynomial (section Toric variety)
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...
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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...
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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...
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featured in the theory of toric varieties, where they correspond to polarized projective toric varieties. For instance, the toric variety corresponding to a...
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In mathematics, a hypertoric variety or toric hyperkähler variety is a quaternionic analog of a toric variety constructed by applying the hyper-Kähler...
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In mathematics, a toric manifold is a topological analogue of toric variety in algebraic geometry. It is an even-dimensional manifold with an effective...
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K-stability (section Toric Varieties)
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...
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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...
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Monomial ideal (redirect from Toric ideal)
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...
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Weighted projective space (redirect from Weighted projective variety)
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...
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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...
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Quiver (mathematics) (section Quiver Variety)
original URL status unknown (link) Quiver representations in toric geometry Projective toric varieties as fine moduli spaces of quiver representations Wikimedia...
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"toric manifolds". However, the term "quasitoric manifold" was eventually adopted to avoid confusion with the class of compact smooth toric varieties,...
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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...
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Singularities of toric varieties give examples of high-dimensional singularities that are easy to resolve explicitly. A toric variety is defined by a fan...
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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...
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projective plane Sphere Spiric section Surface (topology) Toric lens Toric section Toric variety Toroid Toroidal and poloidal Torus-based cryptography Torus...
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Torus action (category Algebraic varieties)
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...
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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...
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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...
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computer-based algebraic geometry (such as Gröbner basis), Torelli sets and toric varieties, and history of mathematics. He is also known for several textbooks...
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H-vector (redirect from Toric h-vector)
"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...
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theory Symbolic method of invariant theory Geometric invariant theory Toric variety Deformation theory Singular point, non-singular Singularity theory Newton...
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an important role in the theory of toric varieties, where it corresponds to projective normality of the toric variety determined by P. Normal polytopes...
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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...
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