complex projective lines
complex projective lines is the plural of complex projective line.
Meaning of complex projective line
Noun
complex projective line (plural complex projective lines)
- A complex line (especially, the set of complex numbers regarded as such) endowed with a point at infinity (thus becoming a projective line); (more formally) the set of equivalence classes of ordered pairs (α, β) of complex numbers, not both zero, with respect to the equivalence relation "(α, β) ≡ (λα, λβ) for all nonzero complex λ".
- By way of an example, we consider in detail the complex projective line #92;C#92;mathbb#123;P#125;¹.[…]Thus via the function w#95;0 the complex projective line #92;C#92;mathbb#123;P#125;¹ becomes identified with the "extended complex plane" (i.e. the ordinary complex plane with an additional "point...
- 2..2.1 Theorem The complex projective line #92;C#92;mathbb#123;P#125;¹ is diffeomorphic to the 2-dimensional sphere S².1985, B. A. Dubrovin, A. T. Fomenko, S. P. Novikov, translated by R. G. Burns, Modern Geometry — Methods and Applications: Part II, Springer, page 18
- Synonyms:
- extended complex numbers, Riemann sphere
Questions about complex projective lines
- What is complex projective lines the plural of?
- Complex projective lines is the plural of complex projective line.
Words near complex projective lines in the dictionary
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Adapted from Wiktionary: complex projective lines (page history and authors); complex projective line (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.
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