[Un critère géométrique pour prescrire les résidus et certaines applications]
Soit une variété complexe compacte et une somme formelle finie -linéaire des diviseurs de . Un théorème de Weil et Kodaira dit que si est kählerienne, alors il existe une forme logarithmique fermé avec un diviseur résiduel si et seulement si est homologue à zéro dans . Nous généralisons leur théorème aux variétès complexes compactes générales. La condition nécessaire et suffisante est décrite par un nouvel invariant appelé -flat class. Dans la deuxième partie de l’article, nous classons toutes les fonctions pluriharmoniques sur une variété algébrique compacte avec des singularités douces.
Let be a compact complex manifold and a -linear finite formal sum of divisors of . A theorem of Weil and Kodaira says that if is Kähler, then there is a closed logarithmic -form with residue divisor if and only if is homologous to zero in . We generalized their theorem to general compact complex manifolds. The necessary and sufficient condition is described by a new invariant called -flat class. In the second part of the paper, we classify all the pluriharmonic functions on a compact algebraic manifold with mild singularities.
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Keywords: Residue, divisor, meromorphic 1-form, pluriharmonic functions
Mot clés : Résidus, diviseur, 1-forme méromorphe, Fonction pluri harmonique
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@article{AIF_2021__71_5_1963_0,
author = {Fang, Hanlong},
title = {A geometric criterion for prescribing residues and some applications},
journal = {Annales de l'Institut Fourier},
pages = {1963--2018},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {71},
number = {5},
year = {2021},
doi = {10.5802/aif.3446},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3446/}
}
TY - JOUR AU - Fang, Hanlong TI - A geometric criterion for prescribing residues and some applications JO - Annales de l'Institut Fourier PY - 2021 SP - 1963 EP - 2018 VL - 71 IS - 5 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3446/ DO - 10.5802/aif.3446 LA - en ID - AIF_2021__71_5_1963_0 ER -
%0 Journal Article %A Fang, Hanlong %T A geometric criterion for prescribing residues and some applications %J Annales de l'Institut Fourier %D 2021 %P 1963-2018 %V 71 %N 5 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3446/ %R 10.5802/aif.3446 %G en %F AIF_2021__71_5_1963_0
Fang, Hanlong. A geometric criterion for prescribing residues and some applications. Annales de l'Institut Fourier, Tome 71 (2021) no. 5, pp. 1963-2018. doi : 10.5802/aif.3446. https://aif.centre-mersenne.org/articles/10.5802/aif.3446/
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