The Briançon-Skoda number of analytic irreducible planar curves
[Le nombre de Briançon-Skoda de courbes analytiques planes et irréductibles]
Sznajdman, Jacob
Annales de l'Institut Fourier, Tome 64 (2014), p. 177-187 / Harvested from Numdam
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Le nombre de Briançon-Skoda d’un anneau R est défini comme le plus petit entier k, tel que pour tout idéal I⊂R et l≥1, 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 I⊂R and l≥1, 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.

Publié le : 2014-01-01
DOI : https://doi.org/10.5802/aif.2843
Classification:  14H20,  32B10
Mots clés: théorème de Briançon-Skoda, paires charactéristiques de Puiseux, nombre de Milnor, courants résiduels 
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     author = {Sznajdman, Jacob},
     title = {The Brian\c con-Skoda number of analytic irreducible planar curves},
     journal = {Annales de l'Institut Fourier},
     volume = {64},
     year = {2014},
     pages = {177-187},
     doi = {10.5802/aif.2843},
     zbl = {06387270},
     mrnumber = {3330545},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2014__64_1_177_0}
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Sznajdman, Jacob. The Briançon-Skoda number of analytic irreducible planar curves. Annales de l'Institut Fourier, Tome 64 (2014) pp. 177-187. doi : 10.5802/aif.2843. http://gdmltest.u-ga.fr/item/AIF_2014__64_1_177_0/

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