projectivization
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English
[edit]Alternative forms
[edit]Etymology
[edit]From projective + -ization.
Noun
[edit]projectivization (plural projectivizations)
- (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.
- 1992, Maks A. Akivis, Alexander M. Shelekhov, translated by Vladislav V. Goldberg, Geometry and Algebra of Multidimensional Three-Webs, Springer, page 11:
- Let us consider the vector space . Its projectivization , is a projective space, which is obtained from , by factorization relative to the collinearity of vectors. The projectivization is a set of straight lines, passing through the point . Under projectivization, the cone becomes a manifold of dimension .
- 1997, M. E. Alferieff (translator), Alexei Kostrikin, Yuri Manin, Linear Algebra and Geometry, Gordon and Breach Science Publishers, Paperback, page 233,
- Therefore, the projectivization is determined only on the complement .
- 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:
- The projectivization of a two-dimensional irregular equation (1.1) is a holomorphic vector field on having a pair of singularities on the fiber (which correspond to the eigenlines of the matrix , 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.
Related terms
[edit]Translations
[edit]specification of a projective space given a vector space
See also
[edit]Further reading
[edit]Blowing up on Wikipedia.Wikipedia
Projective space on Wikipedia.Wikipedia
Algebraic geometry of projective spaces on Wikipedia.Wikipedia