Algebraic geometry/Topology
Milnor and Tjurina numbers for a hypersurface germ with isolated singularity
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 μτn. 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 μτn. Comme application, nous donnons une minoration du nombre de Tjurina en fonction de n et de la multiplicité de f à l'origine.

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DOI: 10.1016/j.crma.2018.07.004
Liu, Yongqiang 1

1 KU Leuven, Department of Mathematics, Celestijnenlaan 200B, 3001 Leuven, Belgium
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Liu, Yongqiang. 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. http://www.numdam.org/articles/10.1016/j.crma.2018.07.004/

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