The Hartogs extension theorem on (n-1)-complete complex spaces - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2007

The Hartogs extension theorem on (n-1)-complete complex spaces

Résumé

Employing Morse theory for the global control of monodromy and the method of analytic discs for local extension, we establish a version of the global Hartogs extension theorem in a singular setting: for every domain D of an (n-1)-complete normal complex space X of pure dimension n >= 2 and for every compact set K in D such that D - K is connected, holomorphic or meromorphic functions in D - K extend holomorphically or meromorphically to D. Normality is an unvavoidable assumption for holomorphic extension, but we show that meromorphic extension holds on a reduced globally irreducible (not necessarily normal) X of pure dimension n >=2 provided that the regular part of D - K is connected.

Dates et versions

hal-00464607 , version 1 (17-03-2010)

Identifiants

Citer

Joel Merker, Egmont Porten. The Hartogs extension theorem on (n-1)-complete complex spaces. 2007. ⟨hal-00464607⟩
76 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More