Lemma 33.34.4 (0BXU)—The Stacks project

Processing math: 100%

Table of contents
Part 2: Schemes
Chapter 33: Varieties
Section 33.34: Projective space
Lemma 33.34.4 (cite)

previous lemma

numberstags

history
statistics
1 tag refers to this tag

Lemma 33.34.4. Let $k$ be a field. Let $Z \subset \mathbf{P}^ n_ k$ be a closed subscheme which has no embedded points such that every irreducible component of $Z$ has dimension $n - 1$ . Then the ideal $I(Z) \subset k[T_0, \ldots , T_ n]$ corresponding to $Z$ is principal.

Proof. This is a special case of Divisors, Lemma 31.31.3. $\square$

Comments (0)

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$ ). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Comments (0)

Post a comment