A d-bar-theoretical proof of Hartogs' extension theorem on (n-1)-complete spaces

Details A d-bar-theoretical proof of Hartogs' extension theorem on (n-1)-complete spaces A d-bar-theoretical proof of Hartogs' extension theorem on (n-1)-complete spaces

2008-11-12

arxiv.org/abs/0811.1963v2

Mathematics

Complex Variables

9 pages

Scientific paper

Let X be a connected normal complex space of dimension n>=2 which is
(n-1)-complete, and let p: M -> X be a resolution of singularities. By use of
Takegoshi's generalization of the Grauert-Riemenschneider vanishing theorem, we
deduce H^1_{cpt}(M,O)=0, which in turn implies Hartogs' extension theorem on X
by the d-bar-technique of Ehrenpreis.

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