no. 7
On the local pseudoconvexity of certain analytic families of ℂ
[Sur la pseudoconvexité locale de certaines familles analytiques de ℂ]
Ohsawa, Takeo1
1 Graduate School of Mathematics Nagoya University 464-8602 Chikusaku Furocho Nagoya (Japan)
Annales de l'Institut Fourier, Tome 68 (2018) no. 7, pp. 2811-2818.

Nous donnons des conditions pour que certaines fonctions analytiques plurisousharmoniques exhaustives sur des variétés faiblement 1-complètes qui sont des fibrés en droites affines au dessus de surfaces de Riemann soient extensibles à des familles analytiques de fonctions plurisousharmoniques exhaustives. Un exemple de famille non-extensible est également présenté.

For a class of weakly 1-complete ℂ bundles over compact Riemann surfaces, for which canonical plurisubharmonic exhaustion functions on the total spaces are known, some cases are described where such functions can be extended to a plurisubharmonic exhaustion function on analytic families of the ℂ bundles. The nonextendable cases are also discussed.

Publié le :
DOI : 10.5802/aif.3226
Classification : 32E40, 32T05
Keywords: plurisubharmonic functions, pseudoconvexity
Mot clés : fonctions plurisousharmoniques, pseudoconvexité

Ohsawa, Takeo 1

1 Graduate School of Mathematics Nagoya University 464-8602 Chikusaku Furocho Nagoya (Japan)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Ohsawa, Takeo. On the local pseudoconvexity of certain analytic families of $\protect \mathbb{C}$. Annales de l'Institut Fourier, Tome 68 (2018) no. 7, pp. 2811-2818. doi : 10.5802/aif.3226. https://aif.centre-mersenne.org/articles/10.5802/aif.3226/

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