A geometric criterion for prescribing residues and some applications
Annales de l'Institut Fourier, Volume 71 (2021) no. 5, pp. 1963-2018.

Let X be a compact complex manifold and D a -linear finite formal sum of divisors of X. A theorem of Weil and Kodaira says that if X is Kähler, then there is a closed logarithmic 1-form with residue divisor D if and only if D is homologous to zero in H 2n-2 (X,). We generalized their theorem to general compact complex manifolds. The necessary and sufficient condition is described by a new invariant called 𝒬-flat class. In the second part of the paper, we classify all the pluriharmonic functions on a compact algebraic manifold with mild singularities.

Soit X une variété complexe compacte et D une somme formelle finie -linéaire des diviseurs de X. Un théorème de Weil et Kodaira dit que si X est kählerienne, alors il existe une 1-forme logarithmique fermé avec un diviseur résiduel D si et seulement si D est homologue à zéro dans H 2n-2 (X,). Nous généralisons leur théorème aux variétès complexes compactes générales. La condition nécessaire et suffisante est décrite par un nouvel invariant appelé 𝒬-flat class. Dans la deuxième partie de l’article, nous classons toutes les fonctions pluriharmoniques sur une variété algébrique compacte avec des singularités douces.

Online First:
Published online:
DOI: 10.5802/aif.3446
Classification: 32J18
Keywords: Residue, divisor, meromorphic 1-form, pluriharmonic functions
Keywords: Résidus, diviseur, 1-forme méromorphe, Fonction pluri harmonique
Fang, Hanlong 1

1 School of Mathematical Sciences Peking University Beijing 100871 (China)
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Fang, Hanlong. A geometric criterion for prescribing residues and some applications. Annales de l'Institut Fourier, Volume 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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