The Stacks project

Definition 53.16.2. Let $k$ be an algebraically closed field. Let $X$ be an algebraic $1$-dimensional $k$-scheme. Let $x \in X$ be a closed point. We say $x$ defines a multicross singularity if the completion $\mathcal{O}_{X, x}^\wedge $ is isomorphic to (53.16.0.1) for some $n \geq 2$. We say $x$ is a node, or an ordinary double point, or defines a nodal singularity if $n = 2$.