Woit · §7.4 Complex projective space
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英文 OCR 草稿
The passage describes the stereographic correspondence between the sphere and the plane.
机器草稿中的相关讨论摘录
is better thought of not as a plane together with a point, but as a sphere (often called the “Riemann sphere”), with the relation to the plane and the point at infinity given by stereographic projection. Here one creates a oneto-one mapping by considering the lines that go from a point on the sphere to the north pole of the sphere. Such lines will intersect the plane in a point, and give a one-to-one mapping between points on the plane and points on the sphere, except for the north pole. Now, the north pole can be identified with the “point at infinity”, and thus the space can be identified with the space . The picture looks like this
Figure 7.2: The complex projective line
中文机译草稿
原文借助球面到平面的投影说明两者之间的一一对应。
机器草稿中的相关讨论摘录
最好不被看作一个平面连同一点，而应被看作一个球面（常称为“黎曼球面”），其与平面及无穷远点的关系由球极投影给出。这里，通过考虑从球面上一点到球面北极的直线，构造出一个一一映射。这样的直线将与平面相交于一点，并在平面上的点与球面上的点之间给出一个一一映射，北极除外。现在，北极可以等同于“无穷远点”，因此空间 可以等同于空间 。图像如下
图 7.2：复射影直线
来源与版本
正文：中文机译草稿
来源版本：2025-10-20
原文位置：§7.4；PDF 页 100；印刷页 83
处理记录：MinerU OCR；machine-translation/deepseek-v4.1-flash
核对状态：中文机译草稿 · 待校对