Multiplicity of complex hypersurface singularities, Rouche' satellites and Zariski's problem

Details Multiplicity of complex hypersurface singularities, Rouche' satellites and Zariski's problem Multiplicity of complex hypersurface singularities, Rouche' satellites and Zariski's problem

2005-09-19

arxiv.org/abs/math/0509409v2

C. R., Math., Acad. Sci. Paris {\bf 344}, no. 10, 631-634 (2007)

Mathematics

Algebraic Geometry

Final version

Scientific paper

10.1016/j.crma.2007.04.005

Soient $f,g\colon (\hbox{\aa C}^n,0) \to (\hbox{\aa C},0)$ des germes de fonctions holomorphes r\'eduits. Nous montrons que $f$ et $g$ ont la m\^eme multiplicit\'e en 0 si et seulement s'il existe des germes r\'eduits $f'$ et $g'$ analytiquement \'equivalents \`a $f$ et $g$, respectivement, tels que $f'$ et $g'$ satisfassent une in\'egalit\'e du type de Rouch\'e par rapport \`a un `petit' cercle g\'en\'erique autour de~0. Comme application, nous donnons une reformulation de la question de Zariski sur la multiplicit\'e et une r\'eponse partielle positive \`a celle--ci.

Affiliated with

Also associated with

No associations

Rating

Multiplicity of complex hypersurface singularities, Rouche' satellites and Zariski's problem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Multiplicity of complex hypersurface singularities, Rouche' satellites and Zariski's problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Multiplicity of complex hypersurface singularities, Rouche' satellites and Zariski's problem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-298302