Uniqueness and factorization of Coleff-Herrera currents

Mats Andersson[1]

  • [1] Department of Mathematics, Chalmers University of Technology and the University of Göteborg, S-412 96 GÖTEBORG SWEDEN

Annales de la faculté des sciences de Toulouse Mathématiques (2009)

  • Volume: 18, Issue: 4, page 651-661
  • ISSN: 0240-2963

Abstract

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We prove a uniqueness result for Coleff-Herrera currents which in particular means that if f = ( f 1 , ... , f m ) defines a complete intersection, then the classical Coleff-Herrera product associated to f is the unique Coleff-Herrera current that is cohomologous to 1 with respect to the operator δ f - ∂ ¯ , where δ f is interior multiplication with f . From the uniqueness result we deduce that any Coleff-Herrera current on a variety Z is a finite sum of products of residue currents with support on Z and holomorphic forms.

How to cite

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Andersson, Mats. "Uniqueness and factorization of Coleff-Herrera currents." Annales de la faculté des sciences de Toulouse Mathématiques 18.4 (2009): 651-661. <http://eudml.org/doc/10122>.

@article{Andersson2009,
abstract = {We prove a uniqueness result for Coleff-Herrera currents which in particular means that if $f=(f_1,\ldots , f_m)$ defines a complete intersection, then the classical Coleff-Herrera product associated to $f$ is the unique Coleff-Herrera current that is cohomologous to $1$ with respect to the operator $\delta _f-\bar\{\partial \}$, where $\delta _f$ is interior multiplication with $f$. From the uniqueness result we deduce that any Coleff-Herrera current on a variety $Z$ is a finite sum of products of residue currents with support on $Z$ and holomorphic forms.},
affiliation = {Department of Mathematics, Chalmers University of Technology and the University of Göteborg, S-412 96 GÖTEBORG SWEDEN},
author = {Andersson, Mats},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {Coleff-Herrera current; Coleff-Herrera product; sheaf of currents; standard extension property; factorization of currents; pure codimension; complete intersection},
language = {eng},
month = {10},
number = {4},
pages = {651-661},
publisher = {Université Paul Sabatier, Toulouse},
title = {Uniqueness and factorization of Coleff-Herrera currents},
url = {http://eudml.org/doc/10122},
volume = {18},
year = {2009},
}

TY - JOUR
AU - Andersson, Mats
TI - Uniqueness and factorization of Coleff-Herrera currents
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2009/10//
PB - Université Paul Sabatier, Toulouse
VL - 18
IS - 4
SP - 651
EP - 661
AB - We prove a uniqueness result for Coleff-Herrera currents which in particular means that if $f=(f_1,\ldots , f_m)$ defines a complete intersection, then the classical Coleff-Herrera product associated to $f$ is the unique Coleff-Herrera current that is cohomologous to $1$ with respect to the operator $\delta _f-\bar{\partial }$, where $\delta _f$ is interior multiplication with $f$. From the uniqueness result we deduce that any Coleff-Herrera current on a variety $Z$ is a finite sum of products of residue currents with support on $Z$ and holomorphic forms.
LA - eng
KW - Coleff-Herrera current; Coleff-Herrera product; sheaf of currents; standard extension property; factorization of currents; pure codimension; complete intersection
UR - http://eudml.org/doc/10122
ER -

References

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  9. Passare (M.).— A calculus for meromorphic currents. J. Reine Angew. Math. 392, p. 37-56 (1988). Zbl0645.32007MR965056
  10. Passare (M.) & Tsikh (A.).— Residue integrals and their Mellin transforms Canad. J. Math. 47, p. 1037-1050 (1995). Zbl0855.44005MR1350649
  11. Passare (M.) & Tsikh (A.) & Yger (A.).— Residue currents of the Bochner-Martinelli type Publ. Mat. 44, p. 85-117 (2000). Zbl0964.32003MR1775747
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