This is also the function field of the projective line.

The simplest example (other than a point) is to take X to be the projective line.

This then loops around to since pencils are a projective line.

Indeed, three points on a projective line determine a fourth by this relation.

This agrees with the projective line being a curve of genus 0 and having p+1 points.

Also, the case of the projective line is special, and hence generally treated differently.

Compare the real projective line, which does not distinguish between + and .

The line at infinity is itself a projective line over the same ground field.

The projective line is a fundamental example of an algebraic curve.

Thus, the base space of the bundle is taken to be the projective line.