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  2. 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 ().

  3. Convex cone - Wikipedia

    en.wikipedia.org/wiki/Convex_cone

    A subset of a vector space over an ordered field is a cone (or sometimes called a linear cone) if for each in and positive scalar in , the product is in . [2] Note that some authors define cone with the scalar α {\displaystyle \alpha } ranging over all non-negative scalars (rather than all positive scalars, which does not include 0). [ 3 ]

  4. Mapping cylinder - Wikipedia

    en.wikipedia.org/wiki/Mapping_cylinder

    In mathematics, specifically algebraic topology, the mapping cylinder [1] of a continuous function between topological spaces and is the quotient = (([,])) / where the denotes the disjoint union, and ~ is the equivalence relation generated by

  5. Cone - Wikipedia

    en.wikipedia.org/wiki/Cone

    A right circular cone and an oblique circular cone A double cone (not shown infinitely extended) 3D model of a cone. A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex that is not contained in the base.

  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. Cone (topology) - Wikipedia

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

    The cone over a closed interval I of the real line is a filled-in triangle (with one of the edges being I), otherwise known as a 2-simplex (see the final example). The cone over a polygon P is a pyramid with base P. The cone over a disk is the solid cone of classical geometry (hence the concept's name). The cone over a circle given by

  9. Nilpotent cone - Wikipedia

    en.wikipedia.org/wiki/Nilpotent_cone

    In mathematics, the nilpotent cone of a finite-dimensional semisimple Lie algebra is the set of elements that act nilpotently in all representations of . In other words, N = { a ∈ g : ρ ( a ) is nilpotent for all representations ρ : g → End ⁡ ( V ) } . {\displaystyle {\mathcal {N}}=\{a\in {\mathfrak {g}}:\rho (a){\mbox{ is nilpotent for ...

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