Parabolicity of the regular locus of complex varieties

Jean Ruppenthal

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arXiv · 1410.6207

Parabolicity of the regular locus of complex varieties

Jean Ruppenthal

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Abstract

The purpose of this note is to show that the regular locus of a complex variety is locally parabolic at the singular set. This yields that the regular locus of a compact complex variety, e.g., of a projective variety, is parabolic. We give also an application to the $L^2$-theory for the $\overline{\partial}$-operator on singular spaces.

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Jean Ruppenthal. 2014-10-22. Parabolicity of the regular locus of complex varieties. https://arxiv.org/abs/1410.6207

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