"projectivization" meaning in All languages combined

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          "ref": "1992, Maks A. Akivis, Alexander M. Shelekhov, translated by Vladislav V. Goldberg, Geometry and Algebra of Multidimensional Three-Webs, Springer, page 11:",
          "text": "Let us consider the vector space T#x5F;p. Its projectivization #x7B;PT#x7D;#x5F;p, is a projective space, which is obtained from T#x5F;p, by factorization relative to the collinearity of vectors. The projectivization #x7B;PT#x7D;#x5F;p is a set of straight lines, passing through the point p. Under projectivization, the cone C(2,r) becomes a manifold S(1,r-1) of dimension r.",
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          "text": "1997, M. E. Alferieff (translator), Alexei Kostrikin, Yuri Manin, Linear Algebra and Geometry, Gordon and Breach Science Publishers, Paperback, page 233,\nTherefore, the projectivization P(f) is determined only on the complement U_f=P(L)P( ker f)."
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          "ref": "2004, Alexey Glutsyuk, “Confluence of singular points and Stokes phenomena”, in Yulij Ilyashenko, Christiane Rousseau, Gert Sabidussi, editors, Normal Forms, Bifurcations and Finiteness Problems in Differential Equations, Kluwer Academic, page 290:",
          "text": "The projectivization of a two-dimensional irregular equation (1.1) is a holomorphic vector field on #x5C;mathbbP¹#x5C;times#x5C;left#x5C;#x7B;#x5C;vertt#x5C;vert#x3C;1#x5C;right#x5C;#x7D; having a pair of singularities on the fiber #x5C;mathbbP¹#x5C;times 0 (which correspond to the eigenlines of the matrix A(0), the coordinate lines in our case).[…]Now the preceding corollary applied to the family of projectivizations says that the horizontal separatrices converge to the sectorial separatrices of the projectivized nonperturbed equation.",
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        "A process (more formally, a mapping) that, given a vector space, specifies an associated projective space; (loosely) the projective space so specified."
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        "(mathematics, algebraic geometry, birational geometry) A process (more formally, a mapping) that, given a vector space, specifies an associated projective space; (loosely) the projective space so specified."
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