After recalling the definitions of the Abel-Radon transformation of currents and of locally residual currents, we show that the Abel-Radon transform of a locally residual current 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 be a domain of the grassmannian variety of complex -planes in , be the corresponding linearly -concave domain of , and be a locally residual current of bidegree . Suppose that the meromorphic -form extends meromorphically to a greater domain of . If is of type , with an analytic subvariety of pure codimension in , and a meromorphic (resp. regular) -form () on , then extends in a unique way as a locally residual current to the domain . In particular, if , then extends as a -closed residual current on . We show in this note that this theorem remains valid for an arbitrary residual current of bidegree , in the particular case where .
@article{ASNSP_2005_5_4_1_27_0, author = {Fabre, Bruno}, title = {Sur la transformation {d'Abel-Radon} des courants localement r\'esiduels}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {27--57}, publisher = {Scuola Normale Superiore, Pisa}, volume = {5e s{\'e}rie, 4}, number = {1}, year = {2005}, mrnumber = {2165402}, zbl = {1170.32305}, language = {fr}, url = {http://www.numdam.org/item/ASNSP_2005_5_4_1_27_0/} }
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 SP - 27 EP - 57 VL - 4 IS - 1 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2005_5_4_1_27_0/ LA - fr ID - ASNSP_2005_5_4_1_27_0 ER -
%0 Journal Article %A Fabre, Bruno %T Sur la transformation d'Abel-Radon des courants localement résiduels %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2005 %P 27-57 %V 4 %N 1 %I Scuola Normale Superiore, Pisa %U http://www.numdam.org/item/ASNSP_2005_5_4_1_27_0/ %G fr %F ASNSP_2005_5_4_1_27_0
Fabre, Bruno. Sur la transformation d'Abel-Radon des courants localement résiduels. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 4 (2005) no. 1, pp. 27-57. http://www.numdam.org/item/ASNSP_2005_5_4_1_27_0/
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