The Stacks project

Projective space is smooth.

Lemma 33.34.1. Let $k$ be a field and $n \geq 0$. Then $\mathbf{P}^ n_ k$ is a smooth projective variety of dimension $n$ over $k$.

Proof. Omitted. $\square$

Comments (1)

Comment #3016 by Brian Lawrence on

Suggested slogan: Projective space over a field is a smooth projective variety.

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View Lemma 33.34.1 as pdf