A projective line over a field is the one-dimensional projective space . Its points have homogeneous coordinates , where and for every nonzero .

The points form a copy of , and the remaining point is the point at infinity. Thus the -rational points of the projective line can be identified with .

The algebraic blow-up of the affine plane at the origin has a projective line as its exceptional divisor.

See also

Algebraic Blow-Up, Exceptional Divisor, Homogeneous Coordinates, Point at Infinity, Projective Space

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References

Coxeter, H. S. M. Projective Geometry, 2nd ed. New York: Springer-Verlag, 1987.The Stacks Project Authors. "Projective Space." §27.13 in The Stacks Project, Tag 01ND, 2026. https://stacks.math.columbia.edu/tag/01ND.

Cite this as:

Weisstein, Eric W. "Projective Line." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ProjectiveLine.html

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