An irreducible germ of holomorphic function at origin is still irreducible around the origin? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T15:08:46Z http://mathoverflow.net/feeds/question/75581 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/75581/an-irreducible-germ-of-holomorphic-function-at-origin-is-still-irreducible-around An irreducible germ of holomorphic function at origin is still irreducible around the origin? MZWang 2011-09-16T08:21:55Z 2011-09-16T12:57:58Z <p>This question comes from Huybrechts's book <em>Complex Geometry, An Introduction</em>. In proposition 1.1.35, the author claims that if $f$ is an irreducible holomorphic germ in $\mathcal{O}_{\mathbf{C}^n,0}$ at the origin of $\mathbf{C}^n$, then for any $z$ sufficiently close to the origin the holomorphic germ induced by $f$ in the local ring of $\mathbf{C}^n$ at z is irreducible. </p> <p>But the proof only shows the claim holds on the complement of a thin subset.</p> <p><strong>Question.</strong> Is the claim true or false? Can anyone give an answer or a reference?</p>