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What is a toric variety Cox?
From Wikipedia, the free encyclopedia. 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.
What is a toric graph?
Toric ideals are a class of binomial ideals with many applications including to integer programming and algebraic statistics. One can associate a toric ideal to a finite simple graph by taking the kernel of the monomial map which sends the edges of the graph to the product of their endpoints.
What is toric power?
A lens with a different focal length and optical power in two orientations, which are perpendicular to each other, is known as a Toric lens. These contact lenses offer you the potential for fluctuating vision which means that they move and rotate a bit in your eyes which makes the eyes feel more comfortable.
Why was algebraic geometry invented?
Algebraic geometry emerged from analytic geometry after 1850 when topology, complex analysis, and algebra were used to study algebraic curves. An algebraic curve C is the graph of an equation f(x, y) = 0, with points at infinity added, where f(x, y) is a polynomial, in two complex variables, that cannot be factored.
Is Toric the same as astigmatism?
Toric contact lenses are designed for people with astigmatism. Toric contact lenses correct for astigmatism issues that arise from a different curvature of the cornea or lens in your eye (referred to as regular astigmatism, corneal astigmatism or lenticular astigmatism).
Is aspheric the same as toric?
aspheric is a design that tries to eliminate distortion and or excess thickness in a lens. Toric is a lens that has cylinder in it which means astigmatism correction and atoric has no cylinder.
What is a toric variety?
Toric variety. 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.
What is the toric variety of a polytope?
The toric variety of the polytope is the toric variety of its fan. A variation of this construction is to take a rational polytope in the dual of N and take the toric variety of its polar set in N. The toric variety has a map to the polytope in the dual of N whose fibers are topological tori.
How do you find the toric variety of a fan?
The toric variety of a fan is given by taking the affine toric varieties of its cones and gluing them together by identifying U σ with an open subvariety of U τ whenever σ is a face of τ. Conversely, every fan of strongly convex rational cones has an associated toric variety.
Why are toric varieties useful for mirror symmetry?
The idea of toric varieties is useful for mirror symmetry because an interpretation of certain data of a fan as data of a polytope leads to a geometric construction of mirror manifolds. Danilov, V. I. (1978), “The geometry of toric varieties”, Akademiya Nauk SSSR I Moskovskoe Matematicheskoe Obshchestvo.