Last Updated：2025/11/25

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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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projectivization

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Source Word

projectivization

Noun

Japanese Meaning

ベクトル空間に対して、その対応する射影空間を定める写像または変換の操作。 / 射影空間へ写像するプロセス、すなわち射影化のこと。

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To study line bundles, we often consider the projectivization of a vector space, which assigns to each nonzero vector a corresponding point in the associated projective space.

Google Translation / DeepL Translation

線束を研究するために、しばしばベクトル空間に対応する射影空間を割り当てる写像を考える。これは各零でないベクトルを対応する射影空間の点に対応させる。

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Sense（1）

Let us consider the vector space T_p. Its projectivization PTₚ, is a projective space, which is obtained from T_p, by factorization relative to the collinearity of vectors. The projectivization PTₚ 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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projectivizations

（ plural ）

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projectivization

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projectivization

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