On the Briançon-Skoda theorem on a singular variety

Mats Andersson[1]; Håkan Samuelsson[1]; Jacob Sznajdman[1]

  • [1] Chalmers University of Technology and the University of Gothenburg Department of Mathematics 412 96 Göteborg (Sweden)

Annales de l’institut Fourier (2010)

  • Volume: 60, Issue: 2, page 417-432
  • ISSN: 0373-0956

Abstract

top
Let Z be a germ of a reduced analytic space of pure dimension. We provide an analytic proof of the uniform Briançon-Skoda theorem for the local ring 𝒪 Z ; a result which was previously proved by Huneke by algebraic methods. For ideals with few generators we also get much sharper results.

How to cite

top

Andersson, Mats, Samuelsson, Håkan, and Sznajdman, Jacob. "On the Briançon-Skoda theorem on a singular variety." Annales de l’institut Fourier 60.2 (2010): 417-432. <http://eudml.org/doc/116276>.

@article{Andersson2010,
abstract = {Let $Z$ be a germ of a reduced analytic space of pure dimension. We provide an analytic proof of the uniform Briançon-Skoda theorem for the local ring $\mathcal\{O\}_Z$; a result which was previously proved by Huneke by algebraic methods. For ideals with few generators we also get much sharper results.},
affiliation = {Chalmers University of Technology and the University of Gothenburg Department of Mathematics 412 96 Göteborg (Sweden); Chalmers University of Technology and the University of Gothenburg Department of Mathematics 412 96 Göteborg (Sweden); Chalmers University of Technology and the University of Gothenburg Department of Mathematics 412 96 Göteborg (Sweden)},
author = {Andersson, Mats, Samuelsson, Håkan, Sznajdman, Jacob},
journal = {Annales de l’institut Fourier},
keywords = {Briançon-Skoda theorem; analytic space; residue current},
language = {eng},
number = {2},
pages = {417-432},
publisher = {Association des Annales de l’institut Fourier},
title = {On the Briançon-Skoda theorem on a singular variety},
url = {http://eudml.org/doc/116276},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Andersson, Mats
AU - Samuelsson, Håkan
AU - Sznajdman, Jacob
TI - On the Briançon-Skoda theorem on a singular variety
JO - Annales de l’institut Fourier
PY - 2010
PB - Association des Annales de l’institut Fourier
VL - 60
IS - 2
SP - 417
EP - 432
AB - Let $Z$ be a germ of a reduced analytic space of pure dimension. We provide an analytic proof of the uniform Briançon-Skoda theorem for the local ring $\mathcal{O}_Z$; a result which was previously proved by Huneke by algebraic methods. For ideals with few generators we also get much sharper results.
LA - eng
KW - Briançon-Skoda theorem; analytic space; residue current
UR - http://eudml.org/doc/116276
ER -

References

top
  1. Mats Andersson, Coleff-Herrera currents, duality, and Noetherian operators Zbl1241.32007
  2. Mats Andersson, A residue criterion for strong holomorphicity Zbl1198.32001
  3. Mats Andersson, Integral representation with weights. I, Math. Ann. 326 (2003), 1-18 Zbl1024.32005MR1981609
  4. Mats Andersson, Residue currents and ideals of holomorphic functions, Bull. Sci. Math. 128 (2004), 481-512 Zbl1086.32005MR2074610
  5. Mats Andersson, Explicit versions of the Briançon-Skoda theorem with variations, Michigan Math. J. 54 (2006), 361-373 Zbl1155.32004MR2252765
  6. Mats Andersson, Integral representation with weights. II. Division and interpolation, Math. Z. 254 (2006), 315-332 Zbl1104.32002MR2262705
  7. Mats Andersson, E. Götmark, Explicit representation of membership of polynomial ideals Zbl1216.32002
  8. Mats Andersson, Håkan Samuelsson, Koppelman formulas and the ∂ ¯ -equation on an analytic space Zbl1227.32010
  9. Mats Andersson, Elizabeth Wulcan, Decomposition of residue currents Zbl1190.32006
  10. Mats Andersson, Elizabeth Wulcan, Residue currents with prescribed annihilator ideals, Ann. Sci. École Norm. Sup. (4) 40 (2007), 985-1007 Zbl1143.32003MR2419855
  11. Carlos A. Berenstein, Roger Gay, Alekos Vidras, Alain Yger, Residue currents and Bezout identities, 114 (1993), Birkhäuser Verlag, Basel Zbl0802.32001MR1249478
  12. Jan-Erik Björk, Residues and 𝒟 -modules, The legacy of Niels Henrik Abel (2004), 605-651, Springer, Berlin Zbl1069.32001MR2077588
  13. Nicolas R. Coleff, Miguel E. Herrera, Les courants résiduels associés à une forme méromorphe, 633 (1978), Springer, Berlin Zbl0371.32007MR492769
  14. David Eisenbud, Commutative algebra, 150 (1995), Springer-Verlag, New York Zbl0819.13001MR1322960
  15. Gennadi Henkin, Mikael Passare, Abelian differentials on singular varieties and variations on a theorem of Lie-Griffiths, Invent. Math. 135 (1999), 297-328 Zbl0932.32012MR1666771
  16. Craig Huneke, Uniform bounds in Noetherian rings, Invent. Math. 107 (1992), 203-223 Zbl0756.13001MR1135470
  17. Eero Hyry, Orlando Villamayor U., A Briançon-Skoda theorem for isolated singularities, J. Algebra 204 (1998), 656-665 Zbl0928.13006MR1624420
  18. M. Jonsson, E. Wulcan, On Bochner-Martinelli residue currents and their annihilator ideals, Ann. Inst. Fourier (Grenoble) 59 (2009), 2119-2142 Zbl1189.32003
  19. M. Lejeune-Jalabert, B. Teissier, J.-J. Risler, Clôture intégrale des idéaux et équisingularité, Ann. Fac. Sci. Toulouse Math. (6) 17 (2008), 781-859 Zbl1171.13005MR2499856
  20. Joseph Lipman, Avinash Sathaye, Jacobian ideals and a theorem of Briançon-Skoda, Michigan Math. J. 28 (1981), 199-222 Zbl0438.13019MR616270
  21. Joseph Lipman, Bernard Teissier, Pseudorational local rings and a theorem of Briançon-Skoda about integral closures of ideals, Michigan Math. J. 28 (1981), 97-116 Zbl0464.13005MR600418
  22. Mikael Passare, August Tsikh, Alain Yger, Residue currents of the Bochner-Martinelli type, Publ. Mat. 44 (2000), 85-117 Zbl0964.32003MR1775747
  23. Håkan Samuelsson, Regularizations of products of residue and principal value currents, J. Funct. Anal. 239 (2006), 566-593 Zbl1111.32005MR2261338
  24. Günter Scheja, Riemannsche Hebbarkeitssätze für Cohomologieklassen, Math. Ann. 144 (1961), 345-360 Zbl0112.38001MR148941
  25. Henri Skoda, Application des techniques L 2 à la théorie des idéaux d’une algèbre de fonctions holomorphes avec poids, Ann. Sci. École Norm. Sup. (4) 5 (1972), 545-579 Zbl0254.32017MR333246
  26. Henri Skoda, Joël Briançon, Sur la clôture intégrale d’un idéal de germes de fonctions holomorphes en un point de C n , C. R. Acad. Sci. Paris Sér. A 278 (1974), 949-951 Zbl0307.32007MR340642
  27. J. Sznajdman, An elementary proof of the Briançon-Skoda theorem Zbl1250.32006
  28. Elizabeth Wulcan, Residue currents of monomial ideals, Indiana Univ. Math. J. 56 (2007), 365-388 Zbl1120.32004MR2305939

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.