Elementary construction of residue currents associated to Cohen–Macaulay ideals
Annales de l'Institut Fourier, Volume 68 (2018) no. 1, pp. 377-391.

For a Cohen–Macaulay ideal of holomorphic functions, we construct by elementary means residue currents whose annihilator is precisely the given ideal. We give two proofs that the currents have the prescribed annihilator, one using the theory of linkage, and another using an explicit division formula involving these residue currents to express the ideal membership.

Pour un idéal Cohen–Macaulay de fonctions holomorphes, nous construisons de manière élémentaire des courants résiduels qui s’annulent précisément sur cet idéal. Nous donnons deux constructions, l’une utilisant la théorie des idéaux en algèbre commutative, et l’autre utilisant des représentations intégrales qui donnent une décomposition dans l’idéal modulo ces courants résiduels.

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DOI: 10.5802/aif.3164
Classification: 32A26,  32A27,  32C30,  32C37,  13C14
Keywords: residue currents, explicit construction, theory of integral representations, duality principle, Cohen–Macaulay ideals
Lärkäng, Richard 1; Mazzilli, Emmanuel 2

1 Chalmers University of Technology and the University of Gothenburg Department of Mathematics 412 96 Göteborg (Sweden)
2 Université Lille 1 Laboratoire Paul Painlevé U.M.R. CNRS 8524 U.F.R. de Mathématiques, cité scientifique F59 655 Villeneuve d’Ascq Cedex (France)
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Lärkäng, Richard; Mazzilli, Emmanuel. Elementary construction of residue currents associated to Cohen–Macaulay ideals. Annales de l'Institut Fourier, Volume 68 (2018) no. 1, pp. 377-391. doi : 10.5802/aif.3164. https://aif.centre-mersenne.org/articles/10.5802/aif.3164/

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