Green functions with analytic singularities

Rashkovskii, Alexander; Sigurdsson, Ragnar

doi:10.1016/j.crma.2005.02.019

Complex Analysis

Green functions with analytic singularities
[Fonctions de Green avec singularités analytiques]

Présenté par : Jean-Pierre Demailly

Rashkovskii, Alexander ¹ ; Sigurdsson, Ragnar ²

¹ Faculty of Science and Technology, University of Stavanger, N-4036 Stavanger, Norway
² Science Institute, University of Iceland, Dunhaga 3, IS-107 Reykjavik, Iceland

Comptes Rendus. Mathématique, Tome 340 (2005) no. 7, pp. 479-482.

Résumé
Abstract

Nous étudions des propriétés d'une fonction de Green avec des singularités determinées par un sous-espace fermé complexe A d'une variété complexe lisse X. Elle est définie comme la plus grande fonction plurisouharmonique u négative vérifiant $u ⩽ \log | ψ | + O (1)$ , où $ψ = (ψ_{1}, \dots, ψ_{m})$ avec $ψ_{1}, \dots, ψ_{m}$ générateurs locaux du faisceau d'idéaux $I_{A}$ de A.

We study properties of a Green function with singularities determined by a closed complex subspace A of a complex manifold X. It is defined as the largest negative plurisubharmonic function u satisfying locally $u ⩽ \log | ψ | + O (1)$ , where $ψ = (ψ_{1}, \dots, ψ_{m})$ with $ψ_{1}, \dots, ψ_{m}$ local generators for the ideal sheaf $I_{A}$ of A.

Reçu le : 2004-06-14
Accepté le : 2005-02-03
Publié le : 2005-03-16

DOI : 10.1016/j.crma.2005.02.019

Affiliations des auteurs :

Rashkovskii, Alexander ¹ ; Sigurdsson, Ragnar ²

¹ Faculty of Science and Technology, University of Stavanger, N-4036 Stavanger, Norway
² Science Institute, University of Iceland, Dunhaga 3, IS-107 Reykjavik, Iceland

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     title = {Green functions with analytic singularities},
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     pages = {479--482},
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Rashkovskii, Alexander; Sigurdsson, Ragnar. Green functions with analytic singularities. Comptes Rendus. Mathématique, Tome 340 (2005) no. 7, pp. 479-482. doi : 10.1016/j.crma.2005.02.019. http://www.numdam.org/articles/10.1016/j.crma.2005.02.019/

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