On Bochner-Martinelli residue currents and their annihilator ideals

Mattias Jonsson[1]; Elizabeth Wulcan[1]

  • [1] University of Michigan Department of Mathematics Ann Arbor MI 48109-1043 (USA)

Annales de l’institut Fourier (2009)

  • Volume: 59, Issue: 6, page 2119-2142
  • ISSN: 0373-0956

Abstract

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We study the residue current R f of Bochner-Martinelli type associated with a tuple f = ( f 1 , ⋯ , f m ) of holomorphic germs at 0 ∈ C n , whose common zero set equals the origin. Our main results are a geometric description of R f in terms of the Rees valuations associated with the ideal ( f ) generated by f and a characterization of when the annihilator ideal of R f equals ( f ) .

How to cite

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Jonsson, Mattias, and Wulcan, Elizabeth. "On Bochner-Martinelli residue currents and their annihilator ideals." Annales de l’institut Fourier 59.6 (2009): 2119-2142. <http://eudml.org/doc/10449>.

@article{Jonsson2009,
abstract = {We study the residue current $R^f$ of Bochner-Martinelli type associated with a tuple $f=(f_1,\dots ,f_m)$ of holomorphic germs at $0\in \mathbf\{C\}^n$, whose common zero set equals the origin. Our main results are a geometric description of $R^f$ in terms of the Rees valuations associated with the ideal $(f)$ generated by $f$ and a characterization of when the annihilator ideal of $R^f$ equals $(f)$.},
affiliation = {University of Michigan Department of Mathematics Ann Arbor MI 48109-1043 (USA); University of Michigan Department of Mathematics Ann Arbor MI 48109-1043 (USA)},
author = {Jonsson, Mattias, Wulcan, Elizabeth},
journal = {Annales de l’institut Fourier},
keywords = {Residue current; annihilator ideal; Rees valuation; residue current},
language = {eng},
number = {6},
pages = {2119-2142},
publisher = {Association des Annales de l’institut Fourier},
title = {On Bochner-Martinelli residue currents and their annihilator ideals},
url = {http://eudml.org/doc/10449},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Jonsson, Mattias
AU - Wulcan, Elizabeth
TI - On Bochner-Martinelli residue currents and their annihilator ideals
JO - Annales de l’institut Fourier
PY - 2009
PB - Association des Annales de l’institut Fourier
VL - 59
IS - 6
SP - 2119
EP - 2142
AB - We study the residue current $R^f$ of Bochner-Martinelli type associated with a tuple $f=(f_1,\dots ,f_m)$ of holomorphic germs at $0\in \mathbf{C}^n$, whose common zero set equals the origin. Our main results are a geometric description of $R^f$ in terms of the Rees valuations associated with the ideal $(f)$ generated by $f$ and a characterization of when the annihilator ideal of $R^f$ equals $(f)$.
LA - eng
KW - Residue current; annihilator ideal; Rees valuation; residue current
UR - http://eudml.org/doc/10449
ER -

References

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