PlanetMath: complex projective line

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complex projective line

(Definition)

Let $\mathbb{C}$ be the set of complex numbers. We define an equivalence relation on $\mathbb{C}^2-\{0,0\}$ by

$\displaystyle (x1,y1) \sim (x2,y2) \Leftrightarrow \exists \lambda \in \mathbb{C}^* \lambda (x1,y1)=(x2,y2)$

(1)

The set $\mathbb{C}^2-\{0,0\}/\sim$ is a projective variety called the complex projective line.

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"complex projective line" is owned by bwebste. [ full author list (4) | owner history (1) ]

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Cross-references: projective variety, equivalence relation, complex numbers
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This is version 4 of complex projective line, born on 2003-10-15, modified 2005-03-08.
Object id is 4818, canonical name is ComplexProjectiveLine.
Accessed 1478 times total.

Classification:

AMS MSC:

08B30 (General algebraic systems :: Varieties :: Injectives, projectives)

Pending Errata and Addenda

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