Lemma 28.15.2 (0BQ3)—The Stacks project

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Table of contents
Part 2: Schemes
Chapter 28: Properties of Schemes
Section 28.15: Local irreducibility
Lemma 28.15.2 (cite)

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Lemma 28.15.2. A normal scheme is geometrically unibranch.

Proof. This follows from the definitions. Namely, a scheme is normal if the local rings are normal domains. It is immediate from the More on Algebra, Definition 15.106.1 that a local normal domain is geometrically unibranch. $\square$

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