About Stability of Irreducibility for Germs of Holomorphic Functions

Abstract

This survey is about irreducibility for germs of a holomorphic functions $f$. I will show that when the dimension of the domain $U$ of this holomorphic function $f$ is greater than 2, the irreducibility of germs are not necessary to be stable. That means, if the germ of $f$ at point $p$ is irreducible in the stalk of holomorphic functions at $p$, this does NOT means there exists an open neighborhood $V\subset U$ of this point $p$, such that for any point $q\in V$, the germ of $f$ at $q$ is irreducible at the stalk of holomorphic functions at $q$