Assume that 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 . 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 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 . 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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@article{CRMATH_2018__356_9_963_0, author = {Liu, Yongqiang}, title = {Milnor and {Tjurina} numbers for a hypersurface germ with isolated singularity}, journal = {Comptes Rendus. Math\'ematique}, pages = {963--966}, publisher = {Elsevier}, volume = {356}, number = {9}, year = {2018}, doi = {10.1016/j.crma.2018.07.004}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2018.07.004/} }
TY - JOUR AU - Liu, Yongqiang TI - Milnor and Tjurina numbers for a hypersurface germ with isolated singularity JO - Comptes Rendus. Mathématique PY - 2018 SP - 963 EP - 966 VL - 356 IS - 9 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2018.07.004/ DO - 10.1016/j.crma.2018.07.004 LA - en ID - CRMATH_2018__356_9_963_0 ER -
%0 Journal Article %A Liu, Yongqiang %T Milnor and Tjurina numbers for a hypersurface germ with isolated singularity %J Comptes Rendus. Mathématique %D 2018 %P 963-966 %V 356 %N 9 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2018.07.004/ %R 10.1016/j.crma.2018.07.004 %G en %F CRMATH_2018__356_9_963_0
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://archive.numdam.org/articles/10.1016/j.crma.2018.07.004/
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