For a class of weakly 1-complete 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 bundles. The nonextendable cases are also discussed.
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.
DOI : https://doi.org/10.5802/aif.3226
Classification: 32E40, 32T05
Keywords: plurisubharmonic functions, pseudoconvexity
@article{AIF_2018__68_7_2811_0,
author = {Ohsawa, Takeo},
title = {On the local pseudoconvexity of certain analytic families of $\protect \mathbb{C}$},
journal = {Annales de l'Institut Fourier},
publisher = {Association des Annales de l'institut Fourier},
volume = {68},
number = {7},
year = {2018},
pages = {2811-2818},
doi = {10.5802/aif.3226},
language = {en},
url = {https://aif.centre-mersenne.org/item/AIF_2018__68_7_2811_0}
}
Ohsawa, Takeo. On the local pseudoconvexity of certain analytic families of $\protect \mathbb{C}$. Annales de l'Institut Fourier, Volume 68 (2018) no. 7, pp. 2811-2818. doi : 10.5802/aif.3226. https://aif.centre-mersenne.org/item/AIF_2018__68_7_2811_0/
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