A d-bar-theoretical proof of Hartogs' Extension Theorem on Stein spaces with isolated singularities

TL;DR

This paper provides a d-bar-theoretical proof of Hartogs' Extension Theorem for Stein spaces with isolated singularities by solving a weighted d-bar-equation on a desingularization.

Contribution

It introduces a novel d-bar-approach to extend Hartogs' theorem to Stein spaces with isolated singularities, expanding classical complex analysis results.

Findings

Proves Hartogs' Extension Theorem on Stein spaces with isolated singularities

Develops a method to solve weighted d-bar-equations with compact support

Extends classical extension results to singular complex spaces

Abstract

Let X be a connected normal Stein space of pure dimension d>=2 with isolated singularities only. By solving a weighted d-bar-equation with compact support on a desingularization of X, we derive Hartogs' Extension Theorem on X by the d-bar-idea due to Ehrenpreis.