Meromorphic function of several variables

Summary

A meromorphic function of several variables is locally a quotient of two holomorphic functions on an open set of $\C^n$. The denominator must not be identically zero. It extends the one-variable notion of a meromorphic function. A new feature for $n \ge 2$ is the presence of points of indeterminacy, where the function has no value at all, not even $\infty$. Meromorphic functions are the natural analogue of rational functions on complex manifolds and analytic spaces.