Definition 27.15.1. 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.

[Chapter IV (6.15.1), EGA4]

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