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  2. Cone - Wikipedia

    en.wikipedia.org/wiki/Cone

    The axis of a cone is the straight line passing through the apex about which the cone has a circular symmetry. In common usage in elementary geometry, cones are assumed to be right circular, i.e., with a circle base perpendicular to the axis. [1] If the cone is right circular the intersection of a plane with the lateral surface is a conic section.

  3. Cone (algebraic geometry) - Wikipedia

    en.wikipedia.org/wiki/Cone_(algebraic_geometry)

    More generally, given a vector bundle (finite-rank locally free sheaf) E on X, if R=Sym(E *) is the symmetric algebra generated by the dual of E, then the cone ⁡ is the total space of E, often written just as E, and the projective cone ⁡ is the projective bundle of E, which is written as ().

  4. Convex cone - Wikipedia

    en.wikipedia.org/wiki/Convex_cone

    In linear algebra, a cone—sometimes called a linear cone for distinguishing it from other sorts of cones—is a subset of a real vector space that is closed under positive scalar multiplication; that is, is a cone if implies for every positive scalar .

  5. Mapping cylinder - Wikipedia

    en.wikipedia.org/wiki/Mapping_cylinder

    with the subscripted cup symbol denoting the equivalence. The mapping cylinder is commonly used to construct the mapping cone, obtained by collapsing one end of the cylinder to a point. Mapping cylinders are central to the definition of cofibrations.

  6. Dual cone and polar cone - Wikipedia

    en.wikipedia.org/wiki/Dual_cone_and_polar_cone

    A cone C in a vector space X is said to be self-dual if X can be equipped with an inner product ⋅,⋅ such that the internal dual cone relative to this inner product is equal to C. [3] Those authors who define the dual cone as the internal dual cone in a real Hilbert space usually say that a cone is self-dual if it is equal to its internal dual.

  7. Recession cone - Wikipedia

    en.wikipedia.org/wiki/Recession_cone

    In mathematics, especially convex analysis, the recession cone of a set is a cone containing all vectors such that recedes in that direction. That is, the set extends ...

  8. Quadric (algebraic geometry) - Wikipedia

    en.wikipedia.org/wiki/Quadric_(algebraic_geometry)

    A singular quadric surface, the cone over a smooth conic curve. If q can be written (after some linear change of coordinates) as a polynomial in a proper subset of the variables, then X is the projective cone over a lower-dimensional quadric. It is reasonable to focus attention on the case where X is not a cone.

  9. Tangent cone - Wikipedia

    en.wikipedia.org/wiki/Tangent_cone

    The definition of the tangent cone can be extended to abstract algebraic varieties, and even to general Noetherian schemes. Let X be an algebraic variety, x a point of X, and (O X,x, m) be the local ring of X at x. Then the tangent cone to X at x is the spectrum of the associated graded ring of O X,x with respect to the m-adic filtration: