About Stability of Irreducibility for Germs of Holomorphic Functions

Details About Stability of Irreducibility for Germs of Holomorphic Functions About Stability of Irreducibility for Germs of Holomorphic Functions

2005-04-11

arxiv.org/abs/math/0504209v1

Mathematics

Complex Variables

3 pages

Scientific paper

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 $q$

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