Green functions with analytic singularities

Alexander Rashkovskii; Ragnar Sigurdsson

doi:10.1016/j.crma.2005.02.019

Complex Analysis

Green functions with analytic singularities

Presented by: Jean-Pierre Demailly

Alexander Rashkovskii ¹; Ragnar Sigurdsson 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, Volume 340 (2005) no. 7, pp. 479-482.

Abstract
Résumé

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.

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.

Received: 2004-06-14
Accepted: 2005-02-03
Published online: 2005-03-16

DOI: 10.1016/j.crma.2005.02.019

Author's affiliations:

Alexander Rashkovskii ¹; Ragnar Sigurdsson 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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     author = {Alexander Rashkovskii and Ragnar Sigurdsson},
     title = {Green functions with analytic singularities},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {479--482},
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     volume = {340},
     number = {7},
     year = {2005},
     doi = {10.1016/j.crma.2005.02.019},
     language = {en},
}

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Alexander Rashkovskii; Ragnar Sigurdsson. Green functions with analytic singularities. Comptes Rendus. Mathématique, Volume 340 (2005) no. 7, pp. 479-482. doi : 10.1016/j.crma.2005.02.019. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.02.019/

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