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Parabolicity of the regular locus of complex varieties


Author: J. Ruppenthal
Journal: Proc. Amer. Math. Soc. 144 (2016), 225-233
MSC (2010): Primary 31C12, 53C20, 32C18, 32C25, 32W05
DOI: https://doi.org/10.1090/proc12718
Published electronically: June 24, 2015
MathSciNet review: 3415591
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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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Additional Information

J. Ruppenthal
Affiliation: Department of Mathematics, University of Wuppertal, Gaußstr. 20, 42119 Wuppertal, Germany
Email: ruppenthal@uni-wuppertal.de

DOI: https://doi.org/10.1090/proc12718
Keywords: Parabolic Riemannian manifold, singular complex spaces, subharmonic functions, $L^2$-theory, $\overline{\partial}$-operator
Received by editor(s): October 22, 2014
Received by editor(s) in revised form: November 23, 2014, and December 4, 2014
Published electronically: June 24, 2015
Communicated by: Franc Forstneric
Article copyright: © Copyright 2015 American Mathematical Society