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. 



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> **Q.** Is it true that $\mathrm{codim}\_X(X\setminus U)\geq 2$?
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Codimension of the non-locally free locus
The answer is yes, assuming $X$ to be *normal*.


See S. Ishii, *Introduction to singularities* ([Zbl 1308.14001](https://zbmath.org/?q=an:1308.14001)), Proposition 5.1.7 p. 83.


