no. 7
Complex Analysis
Green functions with analytic singularities
[Fonctions de Green avec singularités analytiques]
Présenté par : Jean-Pierre Demailly
Rashkovskii, Alexander1 ; Sigurdsson, Ragnar2
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

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=(ψ1,…,ψm) with ψ1,…,ψm local generators for the ideal sheaf IA 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=(ψ1,…,ψm) avec ψ1,…,ψm générateurs locaux du faisceau d'idéaux IA de A.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2005.02.019

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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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

[1] Bierstone, E.; Milman, P. Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant, Invent. Math., Volume 128 (1997) no. 2, pp. 207-302

[2] Demailly, J.-P. Monge–Ampère operators, Lelong numbers and intersection theory (Ancona, V.; Silva, A., eds.), Complex Analysis and Geometry, Univ. Ser. Math., Plenum Press, New York, 1993, pp. 115-193

[3] Edigarian, A. On the product property of pluricomplex Green functions, Proc. Amer. Math. Soc., Volume 125 (1997), pp. 2855-2858

[4] Lárusson, F.; Sigurdsson, R. Plurisubharmonic functions and analytic discs on manifolds, J. Reine Angev. Math., Volume 501 (1998), pp. 1-39

[5] Lárusson, F.; Sigurdsson, R. Plurisubharmonic extremal functions, Lelong numbers and coherent ideal sheaves, Indiana U. Math. J., Volume 48 (1999), pp. 1513-1534

[6] Lárusson, F.; Sigurdsson, R. Plurisubharmonicty of envelopes of disc functionals on manifolds, J. Reine Angew. Math., Volume 555 (2003), pp. 27-38

[7] Lelong, P. Fonction de Green pluricomplexe et lemmes de Schwarz dans les espaces de Banach, J. Math. Pures Appl., Volume 68 (1989), pp. 319-347

[8] Lelong, P.; Rashkovskii, A. Local indicators for plurisubharmonic functions, J. Math. Pures Appl., Volume 78 (1999), pp. 233-247

[9] Rashkovskii, A. Maximal plurisubharmonic functions associated to holomorphic mappings, Indiana U. Math. J., Volume 47 (1998), pp. 297-309

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