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

TL;DR

This paper provides a new proof of Hartogs' extension theorem for (n-1)-complete complex spaces using d-bar techniques and vanishing theorems, expanding the understanding of complex space extensions.

Contribution

It introduces a d-bar-theoretical proof of Hartogs' theorem on (n-1)-complete spaces, utilizing Takegoshi's vanishing theorem and resolution of singularities.

Findings

H^1_{cpt}(M,O)=0 proven using Takegoshi's theorem

Hartogs' extension theorem established on (n-1)-complete spaces

d-bar-technique effectively applied to complex space extension problems

Abstract

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.