no. 6
Generically strongly q-convex complex manifolds
[Variétés complexes génériquement fortement q-convexes]
Napier, Terrence1 ; Ramachandran, Mohan2
1 Lehigh University, Department of Mathematics, Bethlehem PA 18015 (USA)
2 SUNY at Buffalo, Department of Mathematics, Buffalo NY 14214 (USA)
Annales de l'Institut Fourier, Tome 51 (2001) no. 6, pp. 1553-1598.

On suppose que ϕ est une fonction analytique-réelle plurisousharmonique sur une variété complexe connexe et non-compacte X. Le résultat principal démontre que si l’ensemble analytique-réel des points où ϕ n’est pas fortement q-convexe est de dimension 2q+1 ou moins, alors presque tous les sous-niveaux assez grands de ϕ sont des variétés complexes fortement q-convexes. Pour X de dimension 2, c’est un cas spécial d’un théorème de Diederich et Ohsawa. Nous obtenons aussi une version de ce résultat dans le cas où ϕ est analytique réelle avec coins.

Suppose ϕ is a real analytic plurisubharmonic exhaustion function on a connected noncompact complex manifold X. The main result is that if the real analytic set of points at which ϕ is not strongly q-convex is of dimension at most 2q+1, then almost every sufficiently large sublevel of ϕ is strongly q-convex as a complex manifold. For X of dimension 2, this is a special case of a theorem of Diederich and Ohsawa. A version for ϕ real analytic with corners is also obtained.

DOI : 10.5802/aif.1866
Classification : 32E40, 32F10
Keywords: analytic cycles, holomorphically convex, $q$-complete
Mot clés : cycles analytiques, convexe holomorphiquement, $q$ complet

Napier, Terrence 1 ; Ramachandran, Mohan 2

1 Lehigh University, Department of Mathematics, Bethlehem PA 18015 (USA)
2 SUNY at Buffalo, Department of Mathematics, Buffalo NY 14214 (USA) 
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Napier, Terrence; Ramachandran, Mohan. Generically strongly $q$-convex complex manifolds. Annales de l'Institut Fourier, Tome 51 (2001) no. 6, pp. 1553-1598. doi : 10.5802/aif.1866. https://aif.centre-mersenne.org/articles/10.5802/aif.1866/

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