Comptes Rendus
no. 9
Algebraic geometry/Topology
Milnor and Tjurina numbers for a hypersurface germ with isolated singularity
[Nombres de Milnor et Tjurina pour les germes d'hypersurfaces à singularité isolée]

Présenté par : Claire Voisin

Yongqiang Liu1
1 KU Leuven, Department of Mathematics, Celestijnenlaan 200B, 3001 Leuven, Belgium
Comptes Rendus. Mathématique, Volume 356 (2018) no. 9, pp. 963-966.

Assume that f:(Cn,0)→(C,0) is an analytic function germ at the origin with only isolated singularity. Let μ and τ be the corresponding Milnor and Tjurina numbers. We show that μτ≤n. As an application, we give a lower bound for the Tjurina number in terms of n and the multiplicity of f at the origin.

Soit f:(Cn,0)→(C,0) un germe de fonction analytique au voisinage de l'origine avec une seule singularité isolée. Soient μ et τ les nombres de Milnor et Tjurina correspondants. Nous montrons que μτ≤n. Comme application, nous donnons une minoration du nombre de Tjurina en fonction de n et de la multiplicité de f à l'origine.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2018.07.004

Yongqiang Liu 1

1 KU Leuven, Department of Mathematics, Celestijnenlaan 200B, 3001 Leuven, Belgium 
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Yongqiang Liu. Milnor and Tjurina numbers for a hypersurface germ with isolated singularity. Comptes Rendus. Mathématique, Volume 356 (2018) no. 9, pp. 963-966. doi : 10.1016/j.crma.2018.07.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.07.004/

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