Lemma 107.22.8. Let $g \geq 2$. The inclusion

is that of an open dense subset.

Lemma 107.22.8. Let $g \geq 2$. The inclusion

\[ |\mathcal{M}_ g| \subset |\overline{\mathcal{M}}_ g| \]

is that of an open dense subset.

**Proof.**
Since $\overline{\mathcal{M}}_ g \subset \mathcal{C}\! \mathit{urves}^{lci+}$ is open and since $\mathcal{C}\! \mathit{urves}^{smooth} \cap \overline{\mathcal{M}}_ g = \mathcal{M}_ g$ this follows immediately from Lemma 107.17.1.
$\square$

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