Topic
Toric variety
About: Toric variety is a research topic. Over the lifetime, 2630 publications have been published within this topic receiving 65604 citations. The topic is also known as: torus embedding.
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25 Apr 2001TL;DR: A 'pear' shape modeling is presented and Bezier-like control point schemes for toric surfaces are defined via mixed trigonometric-polynomial parametrizations.
Abstract: We present an informal introduction to the theory of toric surfaces from the viewpoint of geometric modeling. Bezier surfaces and many well-known low-degree rational surfaces are found to be toric. Bezier like control point schemes for toric surfaces are defined via mixed trigonometric- polynomial parametrizations. Many examples are considered: quadrics, cubic Mobius strip, quartic 'pillow', 'cross-cap' and Dupin cyclides. A 'pear' shape modeling is presented.
15 citations
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TL;DR: In this article, a conjectural ring structure on the intersection cohomology of a hypertoric variety is introduced, which is a quaternionic analogue of a toric variety, and it is shown that the topology of hypertoric varieties interacts richly with the combinatorics of hyperplane arrangements and matroids.
Abstract: A hypertoric variety is a quaternionic analogue of a toric variety. Just as the topology of toric varieties is closely related to the combinatorics of polytopes, the topology of hypertoric varieties interacts richly with the combinatorics of hyperplane arrangements and matroids. Using finite field methods, we obtain combinatorial descriptions of the Betti numbers of hypertoric varieties, both for ordinary cohomology in the smooth case and intersection cohomology in the singular case. We also introduce a conjectural ring structure on the intersection cohomology of a hypertoric variety.
15 citations
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TL;DR: In this article, a singular symplectic toric manifold with the image of the moment map is constructed from M====== n>>\s, from which a manifold can be constructed with the same action.
Abstract: Let M
n
be the moduli space of spatial polygons with n edges. An open dense subset of M
n
admits a T
n−3 -action, although this action does not extend to M
n
. The action together with a symplectic structure on M
n
naturally defines a convex polytope Δ
n
in ℝ
n−3. In this paper, from M
n
, we construct a singular symplectic toric manifold with Δ
n
as the image of the moment map.
15 citations
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15 citations
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TL;DR: In this article, the splitting of the Frobenius direct image of line bundles on toric varieties is used to explicitly construct an orthogonal basis for line bundles in the derived category D b (X) where X is a Fano toric variety with (almost) maximal Picard number.
Abstract: O-ROIG �� Abstract. In this paper, we will use the splitting of the Frobenius direct image of line bundles on toric varieties to explicitly construct an orthogonal basis of line bundles in the derived category D b (X) where X is a Fano toric variety with (almost) maximal Picard number.
15 citations