Algebraic geometry

Toric variety

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. (Wikipedia).

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Projective space | Smooth scheme | Affine space | Basis (universal algebra) | Free abelian group | GIT quotient | Mirror symmetry (string theory) | Gordan's lemma | Combinatorics | Quotient stack | Toric stack | Convex cone | Algebraic geometry | Toroidal embedding | Algebraic variety | Resolution of singularities | Complex projective plane | Algebraic torus