The Stacks project

Definition 109.22.4. 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 109.22.3. 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 109.22.5.