0
$\begingroup$

Let $X$ be a projective scheme over some field $k$. Let $\mathcal{L}$ be an ample invertible sheaf on $X$ and let $s \in \mathcal{L}(X)$ denote a global section of $\mathcal{L}$. Let $X_s = \{P \in X \mid s_P\mathcal{O}_{X,P} \cong \mathcal{L}_P\}$ be open. I am looking for a reference that $\operatorname{codim}(X\setminus X_s, X) \leq 1$ holds.

$\endgroup$
  • 1
    $\begingroup$ $X_s$ could be empty. $\endgroup$ – Mohan Sep 5 '18 at 18:24
  • $\begingroup$ @Mohan Do you know a reference for the edited question/statement? $\endgroup$ – windsheaf Sep 6 '18 at 6:27
  • $\begingroup$ the problem at hand had nothing to do with the scheme being projective or not .. $\endgroup$ – skeptic Sep 6 '18 at 7:15
  • $\begingroup$ @skeptic Okay. However, do you know a reference? $\endgroup$ – windsheaf Sep 6 '18 at 7:17
  • $\begingroup$ have a look at krulls principal ideal theorem $\endgroup$ – skeptic Sep 6 '18 at 7:24

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.