4
$\begingroup$

Let $X$ be a Noetherian, integral scheme. Let $\mathcal{F}$ be a torsion free sheaf on $X$ and let $U \subseteq X$ be the open subscheme where $\mathcal{F}$ is locally free.

Q. Is it true that $\mathrm{codim}_X(X\setminus U)\geq 2$?

$\endgroup$
6
$\begingroup$

The answer is yes, assuming $X$ to be normal.

See S. Ishii, Introduction to singularities (Zbl 1308.14001), Proposition 5.1.7 p. 83.

| cite | improve this answer | |
$\endgroup$

Your Answer

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