The Stacks project

Definition 28.15.1. Let $X$ be a scheme. Let $x \in X$. We say $X$ is unibranch at $x$ if the local ring $\mathcal{O}_{X, x}$ is unibranch. We say $X$ is geometrically unibranch at $x$ if the local ring $\mathcal{O}_{X, x}$ is geometrically unibranch. We say $X$ is unibranch if $X$ is unibranch at all of its points. We say $X$ is geometrically unibranch if $X$ is geometrically unibranch at all of its points.