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

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dc.creatorMerker, Joel
dc.creatorPorten, Egmont
dc.date2007-04-24
dc.date.accessioned2026-07-07T07:58:00Z
dc.date.available2026-07-07T07:58:00Z
dc.descriptionEmploying 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.
dc.description19 pages, 5 figures
dc.identifierhttps://arxiv.org/abs/0704.3216
dc.identifierhttp://arxiv.org/abs/0704.3216
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/127853
dc.subjectComplex Variables
dc.subjectDifferential Geometry
dc.subject32F10, 32C20, 32C55
dc.titleThe Hartogs extension theorem on (n-1)-complete complex spaces
dc.typetext

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