narrowly to either a convex cone or projective cone. Cones can be generalized to higher dimensions. The perimeter of the base of a cone is called the directrix...

A projective cone (or just cone) in projective geometry is the union of all lines that intersect a projective subspace R (the apex of the cone) and an...

Mapping cone (homological algebra) Cone (topology) Projective cone, the union of all lines that intersect a projective subspace and an arbitrary subset...

\mathbb {P} (C)=\operatorname {Proj} _{X}R} is called the projective cone of C or R. Note: The cone comes with the G m {\displaystyle \mathbb {G} _{m}} -action...

Cone snails, or cones, are highly venomous sea snails that constitute the family Conidae. Conidae is a taxonomic family (previously subfamily) of predatory...

normal bundle to X in Y is the tangent bundle to X. The normal cone (or rather its projective cousin) appears as a result of blow-up. Precisely, let π : Bl...

the projective cone of a smooth variety: given a smooth projective variety X ⊂ P n {\displaystyle X\subset \mathbb {P} ^{n}} its projective cone is the...

{\displaystyle \pi } . A projective mapping is a finite sequence of perspective mappings. As a projective mapping in a projective plane over a field (pappian...

Traffic cones, also called pylons, witches' hats, road cones, highway cones, safety cones, caution cones, channelizing devices, construction cones, roadworks...

complex projective space is the projective space with respect to the field of complex numbers. By analogy, whereas the points of a real projective space...

In mathematics, a projective bundle is a fiber bundle whose fibers are projective spaces. By definition, a scheme X over a Noetherian scheme S is a Pn-bundle...

by working in projective space rather than affine space. An example is the quadric surface x y = z w {\displaystyle xy=zw} in projective space P 3 {\displaystyle...

affine algebraic set. Quadrics may also be defined in projective spaces; see § Normal form of projective quadrics, below. In coordinates x1, x2, ..., xD+1...

planes. In projective geometry, a specific instance of this problem that has numerous applications is determining whether, and how, a projective space can...

of toric varieties are affine space, projective spaces, products of projective spaces and bundles over projective space. The original motivation to study...

projective variety is nef if it has nonnegative degree on every curve in the variety. The classes of nef line bundles are described by a convex cone,...

y 4 + z 4 + w 4 = 0 {\textstyle x^{4}+y^{4}+z^{4}+w^{4}=0} in complex projective 3-space. Together with two-dimensional compact complex tori, K3 surfaces...

In algebraic geometry, a projective variety is an algebraic variety that is a closed subvariety of a projective space. That is, it is the zero-locus in...

the projective plane with homogeneous coordinates (a:b:c). The dual curve is a curve in the projective tangent space at the point, and the affine cone over...

being ruled or doubly ruled are preserved by projective maps, and therefore are concepts of projective geometry. In algebraic geometry, ruled surfaces...

simplified by working in projective space rather than affine space, and so cubic surfaces are generally considered in projective 3-space P 3 {\displaystyle...

In project management, the cone of uncertainty describes the evolution of the amount of best case uncertainty during a project. At the beginning of a...

Mori's version of the theorem is as follows: Cone Theorem. Let X {\displaystyle X} be a smooth projective variety. Then 1. There are countably many rational...

fundamental geometric statement on projective spaces: the Euler sequence. The negativity of the canonical line bundle makes projective spaces prime examples of...

icosahedron cones and cylinders the sphere other quadrics: spheroid, ellipsoid, paraboloid and hyperboloids. Advanced topics include: projective geometry...

Spheroid Ellipsoid Hyperboloid Paraboloid Cone Torus Root system Similarity Zonotope Projective geometry Arc (projective geometry) Desargues' theorem Girard...

electric fields. In some projective planes, it is possible to find geometric transformations that map each point of the projective plane to a line, and each...

those of inversive geometry. The projective model identifies the conformal sphere with a certain quadric in a projective space. Let q denote the Lorentzian...

A conifer cone, or in formal botanical usage a strobilus, pl.: strobili, is a seed-bearing organ on gymnosperm plants, especially in conifers and cycads...

a projectivity (projective transformation, projective collineation and homography are synonyms). There are several results concerning projectivities and...