Sur la transformation d’Abel-Radon des courants localement résiduels

Bruno Fabre[1]

  • [1] 22, rue Emile Dubois 75014 Paris, France

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2005)

  • Volume: 4, Issue: 1, page 27-57
  • ISSN: 0391-173X

Abstract

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After recalling the definitions of the Abel-Radon transformation of currents and of locally residual currents, we show that the Abel-Radon transform ℛ ( α ) of a locally residual current α remains locally residual. Then a theorem of P. Griffiths, G. Henkin and M. Passare (cf. [7], [9] and [10]) can be formulated as follows  :Let U be a domain of the grassmannian variety G ( p , N ) of complex p -planes in N , U * : = ∪ t ∈ U H t be the corresponding linearly p -concave domain of N , and α be a locally residual current of bidegree ( N , p ) . Suppose that the meromorphic n -form ℛ ( α ) extends meromorphically to a greater domain U ˜ of G ( p , N ) . If α is of type ω ∧ [ T ] , with T an analytic subvariety of pure codimension p in U * , and ω a meromorphic (resp. regular) q -form ( q > 0 ) on T , then α extends in a unique way as a locally residual current to the domain U ˜ * : = ∪ t ∈ U ˜ H t . In particular, if ℛ ( α ) = 0 , then α extends as a ∂ ¯ -closed residual current on N .We show in this note that this theorem remains valid for an arbitrary residual current of bidegree ( N , p ) , in the particular case where p = 1 .

How to cite

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Fabre, Bruno. "Sur la transformation d’Abel-Radon des courants localement résiduels." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 4.1 (2005): 27-57. <http://eudml.org/doc/84555>.

@article{Fabre2005,
affiliation = {22, rue Emile Dubois 75014 Paris, France},
author = {Fabre, Bruno},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {fre},
number = {1},
pages = {27-57},
publisher = {Scuola Normale Superiore, Pisa},
title = {Sur la transformation d’Abel-Radon des courants localement résiduels},
url = {http://eudml.org/doc/84555},
volume = {4},
year = {2005},
}

TY - JOUR
AU - Fabre, Bruno
TI - Sur la transformation d’Abel-Radon des courants localement résiduels
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2005
PB - Scuola Normale Superiore, Pisa
VL - 4
IS - 1
SP - 27
EP - 57
LA - fre
UR - http://eudml.org/doc/84555
ER -

References

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