Definition 99.13.1. Let $\mathcal{X}$ be an algebraic stack. Let $x \in |\mathcal{X}|$.

1. The number of geometric branches of $\mathcal{X}$ at $x$ is either $n \in \mathbf{N}$ if the equivalent conditions of Lemma 99.7.4 hold for $\mathcal{P}_ n$ defined above, or else $\infty$.

2. We say $\mathcal{X}$ is geometrically unibranch at $x$ if the number of geometric branches of $\mathcal{X}$ at $x$ is $1$.

There are also:

• 4 comment(s) on Section 99.13: Local irreducibility

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).