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

2007/04/24 by Merker, Joel, Porten, Egmont
#32C20 #32C55 #32F10 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0704.3216

Abstract

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.

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