Definition 53.19.1. Let $k$ be a field. Let $X$ be a $1$-dimensional locally algebraic $k$-scheme.

We say a closed point $x \in X$ is a

*node*, or an*ordinary double point*, or*defines a nodal singularity*if there exists an ordinary double point $\overline{x} \in X_{\overline{k}}$ mapping to $x$.We say the

*singularities of $X$ are at-worst-nodal*if all closed points of $X$ are either in the smooth locus of the structure morphism $X \to \mathop{\mathrm{Spec}}(k)$ or are ordinary double points.

## Comments (0)