Generically strongly <span class="mathjax-formula">$q$</span>-convex complex manifolds

Napier, Terrence; Ramachandran, Mohan

doi:10.5802/aif.1866

Generically strongly

q

-convex complex manifolds
[Variétés complexes génériquement fortement

q

-convexes]

Napier, Terrence ; Ramachandran, Mohan

Annales de l'Institut Fourier, Tome 51 (2001) no. 6, pp. 1553-1598.

Résumé
Abstract

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 $2 q + 1$ 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 $2 q + 1$ , 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.

MR 1870640 | Zbl 0996.32004

DOI : https://doi.org/10.5802/aif.1866
Classification : 32E40, 32F10
Mots clés : cycles analytiques, convexe holomorphiquement,

q

complet

BibTeX
RIS

@article{AIF_2001__51_6_1553_0,
     author = {Napier, Terrence and Ramachandran, Mohan},
     title = {Generically strongly $q$-convex complex manifolds},
     journal = {Annales de l'Institut Fourier},
     pages = {1553--1598},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {51},
     number = {6},
     year = {2001},
     doi = {10.5802/aif.1866},
     zbl = {0996.32004},
     mrnumber = {1870640},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.1866/}
}

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AU  - Napier, Terrence
AU  - Ramachandran, Mohan
TI  - Generically strongly $q$-convex complex manifolds
JO  - Annales de l'Institut Fourier
PY  - 2001
DA  - 2001///
SP  - 1553
EP  - 1598
VL  - 51
IS  - 6
PB  - Association des Annales de l’institut Fourier
UR  - http://www.numdam.org/articles/10.5802/aif.1866/
UR  - https://zbmath.org/?q=an%3A0996.32004
UR  - https://www.ams.org/mathscinet-getitem?mr=1870640
UR  - https://doi.org/10.5802/aif.1866
DO  - 10.5802/aif.1866
LA  - en
ID  - AIF_2001__51_6_1553_0
ER  -

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. http://www.numdam.org/articles/10.5802/aif.1866/

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