Local dimension of an algebraic variety
= Local dimension of an algebraic variety
{title2=$\dim\mathcal O_{X,x}$}
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.