The Stacks project

Definition 109.16.4. We denote $\mathcal{M}$ and we name it the moduli stack of smooth proper curves the algebraic stack $\mathcal{C}\! \mathit{urves}^{smooth, h0}$ parametrizing families of curves introduced in Lemma 109.16.3. For $g \geq 0$ we denote $\mathcal{M}_ g$ and we name it the moduli stack of smooth proper curves of genus $g$ the algebraic stack introduced in Lemma 109.16.5.