The Briançon-Skoda number of analytic irreducible planar curves

Jacob Sznajdman[1]

  • [1] Chalmers University of Technology and University of Gothenburg Mathematical Sciences S-412 96 Gothenburg (Suède)

Annales de l’institut Fourier (2014)

  • Volume: 64, Issue: 1, page 177-187
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Sznajdman, Jacob. "The Briançon-Skoda number of analytic irreducible planar curves." Annales de l’institut Fourier 64.1 (2014): 177-187. <http://eudml.org/doc/275660>.

@article{Sznajdman2014,
abstract = {The Briançon-Skoda number of a ring $R$ is defined as the smallest integer k, such that for any ideal $I\subset R$ and $l\ge 1$, 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.},
affiliation = {Chalmers University of Technology and University of Gothenburg Mathematical Sciences S-412 96 Gothenburg (Suède)},
author = {Sznajdman, Jacob},
journal = {Annales de l’institut Fourier},
keywords = {Briançon-Skoda theorem; Puiseux pairs; Milnor number; residue currents},
language = {eng},
number = {1},
pages = {177-187},
publisher = {Association des Annales de l’institut Fourier},
title = {The Briançon-Skoda number of analytic irreducible planar curves},
url = {http://eudml.org/doc/275660},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Sznajdman, Jacob
TI - The Briançon-Skoda number of analytic irreducible planar curves
JO - Annales de l’institut Fourier
PY - 2014
PB - Association des Annales de l’institut Fourier
VL - 64
IS - 1
SP - 177
EP - 187
AB - The Briançon-Skoda number of a ring $R$ is defined as the smallest integer k, such that for any ideal $I\subset R$ and $l\ge 1$, 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.
LA - eng
KW - Briançon-Skoda theorem; Puiseux pairs; Milnor number; residue currents
UR - http://eudml.org/doc/275660
ER -

References

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