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

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

How to cite

top

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

top
  1. Andersson (M.).— Residue currents and ideals of holomorphic functions Bull. Sci. Math., 128, p. 481-512 (2004). Zbl1086.32005MR2074610
  2. Andersson (M.) & Wulcan (E.).— Decomposition of residue currents J. Reine Angew. Math. (to appear). Zbl1190.32006
  3. Barlet (D.).— Fonctions de type trace Ann. Inst. Fourier 33, p. 43-76 (1983). Zbl0498.32002MR699486
  4. Björk (J-E) Residue calculus and -modules om complex manifolds Preprint Stockholm (1996). 
  5. Björk (J-E).— Residues and -modules The legacy of Niels Henrik Abel, 605–651, Springer, Berlin, 2004. Zbl1069.32001MR2077588
  6. Coleff (N.r.) & Herrera (M.e.).— Les courants résiduels associés à une forme méromorphe Lect. Notes in Math. 633, Berlin-Heidelberg-New York (1978). Zbl0371.32007MR492769
  7. Dickenstein (A.) & Sessa (C.).— Canonical representatives in moderate cohomology Invent. Math. 80, p. 417-434 (1985). Zbl0556.32005MR791667
  8. Passare (M.).— Residues, currents, and their relation to ideals of holomorphic functions Math. Scand. 62, p. 75-152 (1988). Zbl0633.32005MR961584
  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
  12. Samuelsson (H.).— Regularizations of products of residue and principal value currents J. Funct. Anal. 239, p. 566-593 (2006). Zbl1111.32005MR2261338

NotesEmbed ?

top

You must be logged in to post comments.