Sznajdman, Jacob
The Briançon-Skoda number of analytic irreducible planar curves  [ Le nombre de Briançon-Skoda de courbes analytiques planes et irréductibles ]
Annales de l'institut Fourier, Tome 64 (2014) no. 1 , p. 177-187
MR 3330545 | Zbl 06387270
doi : 10.5802/aif.2843
URL stable : http://www.numdam.org/item?id=AIF_2014__64_1_177_0

Classification:  14H20,  32B10
Mots clés: théorème de Briançon-Skoda, paires charactéristiques de Puiseux, nombre de Milnor, courants résiduels
Le nombre de Briançon-Skoda d’un anneau R est défini comme le plus petit entier k, tel que pour tout idéal IR et l1, la clôture intégrale de I k+l-1 est contenu dans I l . Nous calculons le nombre de Briançon-Skoda de l’anneau local d’une courbe analytique plane et irréductible en fonction de ses exposants caractéristiques de Puiseux. Il s’avère que ce nombre est étroitement lié au nombre de Milnor.
The Briançon-Skoda number of a ring R is defined as the smallest integer k, such that for any ideal IR and l1, the integral closure of I k+l-1 is contained in I l . We compute the Briançon-Skoda number of the local ring of any analytic irreducible planar curve in terms of its Puiseux characteristics. It turns out that this number is closely related to the Milnor number.

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