The Stacks project

Definition 66.23.2. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. Let $x \in |X|$. We say that $X$ is geometrically unibranch at $x$ if the equivalent conditions of Lemma 66.23.1 hold. We say that $X$ is geometrically unibranch if $X$ is geometrically unibranch at every $x \in |X|$.