The membership problem for polynomial ideals in terms of residue currents

Mats Andersson[1]

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

Annales de l’institut Fourier (2006)

  • Volume: 56, Issue: 1, page 101-119
  • ISSN: 0373-0956

Abstract

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We find a relation between the vanishing of a globally defined residue current on ℙ n and solution of the membership problem with control of the polynomial degrees. Several classical results appear as special cases, such as Max Nöther’s theorem, for which we also obtain a generalization. Furthermore there are some connections to effective versions of the Nullstellensatz. We also provide explicit integral representations of the solutions.

How to cite

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Andersson, Mats. "The membership problem for polynomial ideals in terms of residue currents." Annales de l’institut Fourier 56.1 (2006): 101-119. <http://eudml.org/doc/10135>.

@article{Andersson2006,
abstract = {We find a relation between the vanishing of a globally defined residue current on $\mathbb\{P\}^n$ and solution of the membership problem with control of the polynomial degrees. Several classical results appear as special cases, such as Max Nöther’s theorem, for which we also obtain a generalization. Furthermore there are some connections to effective versions of the Nullstellensatz. We also provide explicit integral representations of the solutions.},
affiliation = {Chalmers University of Technology and the University of Göteborg Department of Mathematics 412 96 Göteborg (Sweden)},
author = {Andersson, Mats},
journal = {Annales de l’institut Fourier},
keywords = {membership problem; polynomial ideal; residue current; integral representation; integral representations},
language = {eng},
number = {1},
pages = {101-119},
publisher = {Association des Annales de l’institut Fourier},
title = {The membership problem for polynomial ideals in terms of residue currents},
url = {http://eudml.org/doc/10135},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Andersson, Mats
TI - The membership problem for polynomial ideals in terms of residue currents
JO - Annales de l’institut Fourier
PY - 2006
PB - Association des Annales de l’institut Fourier
VL - 56
IS - 1
SP - 101
EP - 119
AB - We find a relation between the vanishing of a globally defined residue current on $\mathbb{P}^n$ and solution of the membership problem with control of the polynomial degrees. Several classical results appear as special cases, such as Max Nöther’s theorem, for which we also obtain a generalization. Furthermore there are some connections to effective versions of the Nullstellensatz. We also provide explicit integral representations of the solutions.
LA - eng
KW - membership problem; polynomial ideal; residue current; integral representation; integral representations
UR - http://eudml.org/doc/10135
ER -

References

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