The Stacks project

Lemma 109.10.2. We have $\mathcal{C}\! \mathit{urves}^{geomred} \subset \mathcal{C}\! \mathit{urves}^{CM}$ as open substacks of $\mathcal{C}\! \mathit{urves}$.

Proof. This is true because a reduced Noetherian scheme of dimension $\leq 1$ is Cohen-Macaulay. See Algebra, Lemma 10.157.3. $\square$

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