On the local pseudoconvexity of certain analytic families of $ℂ$

Ohsawa, Takeo

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.

Classification : 32E40, 32T05
Keywords: plurisubharmonic functions, pseudoconvexity
Mot clés : fonctions plurisousharmoniques, pseudoconvexité

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