Example

\* Let X be a complex algebraic variety, $\mathscr{O}_{X,x}$ the local ring of X at a rational point x, $X^{an}$ the analytic space associated with X; let x again denote the point of $X^{an}$ corresponding to x, and let $\mathscr{O}_{X^{an},x}$ be the local ring of $X^{an}$ at x. Then $e(\mathscr{O}_{X^{an},x}) = e(\mathscr{O}_{X,x})$. \*