Definition 33.46.1. Let $k$ be an algebraically closed field. Let $X$ be a locally algebraic $k$-scheme and let $x \in X$ be a closed point. The embedding dimension of $X$ at $x$ is $\dim _ k \mathfrak m_ x/\mathfrak m_ x^2$.

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).