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complex projective line
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(Definition)
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Let $\mathbb C$ be the set of complex numbers. We define an equivalence relation on $\mathbb C^2-\{0,0\}$ by \begin{equation} (x1,y1) \sim (x2,y2) \Leftrightarrow \exists \lambda \in \mathbb C^* \lambda (x1,y1)=(x2,y2) \end{equation} 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
There are 2 references to this entry.
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 1979 times total.
Classification:
| AMS MSC: | 08B30 (General algebraic systems :: Varieties :: Injectives, projectives) |
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Pending Errata and Addenda
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