I have seen in several places that, given a holomorphic map $F:M^m \rightarrow N^n$ between complex manifolds, the level sets of $F$ support(/are) subvarieties. That is, for any $y \in N$ the set $F^{-1}(y) \subset M$ is a subvariety of $M$.
I would like to know how to prove this precisely, in fact I would like to know as many different ways to prove this as possible.
There are a few questions along these lines on this site but I wanted a clarification on this.