Morse equi-singular deformation in $\mathbb{C}^2$

C. R. Math. Rep. Acad. Sci. Canada Vol. 32 (4) 2010, pp. 120–126

December 30, 2010

Tzee-Char Kuo, School of Mathematics, University of Sydney, Sydney, NSW, 2006 Austrial; e-mail: tck@maths.usyd.edu.au

Laurentiu Paunescu, School of Mathematics, University of Sydney, Sydney, NSW, 2006 Austrial; e-mail: laurent@maths.usyd.edu.au

Abstract/Résumé:

The enriched complex line $\mathbb{C}_*$ is $\mathbb{C}$ plus a set of infinitesimals. The Morse stability notion is used for an equi-singular deformation theorem in $\mathbb{C}\{x,y\}$ ($=\mathcal{O}_2$).

On appelle la droite complexe enrichie $C_*$, la réunion de la droite complexe $\mathbb{C}_*$ avec un ensemble des infinitésimaux. La notion de stabilité de Morse est appliquée au théorème de déformation equisingulière dans $\mathbb{C}\{x,y\}$ ($=\mathcal{O}_2$).

Keywords:
AMS Subject Classification: Curves 14Hxx

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