Definition 108.22.4. We denote $\overline{\mathcal{M}}$ and we name the *moduli stack of stable curves* the algebraic stack $\mathcal{C}\! \mathit{urves}^{stable}$ parametrizing stable families of curves introduced in Lemma 108.22.3. For $g \geq 2$ we denote $\overline{\mathcal{M}}_ g$ and we name the *moduli stack of stable curves of genus $g$* the algebraic stack introduced in Lemma 108.22.5.

[DM]

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