Local dimension of an algebraic variety ($\dim {\mathcal{O}}_{X,x}$)

The Krull dimension of ${\mathcal{O}}_{X,x}$ at a point $x$. For a closed point of an irreducible affine variety it equals $\dim X$, by the closed-point dimension lemma for affine domains. At a generic point of a codimension-one subvariety the local dimension is one.