The Hartogs extension problem for holomorphic parabolic and reductive geometries

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• 作者：Benjamin McKay
• 关键词：Cartan geometry ; Hartogs extension ; Hopf manifold
• 刊名：Monatshefte f¨¹r Mathematik
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：181
• 期：3
• 页码：689-713
• 全文大小：568 KB
• 刊物主题：Mathematics, general;
• 出版者：Springer Vienna
• ISSN：1436-5081
• 卷排序：181

文摘

Every holomorphic effective parabolic or reductive geometry on a domain over a Stein manifold is the pullback of a unique such geometry on the envelope of holomorphy of the domain. We use this result to classify the Hopf manifolds which admit holomorphic reductive geometries, and to classify the Hopf manifolds which admit holomorphic parabolic geometries. Every Hopf manifold which admits a holomorphic parabolic geometry with a given model admits a flat one. We classify flat holomorphic parabolic geometries on Hopf manifolds. For every generalized flag manifold there is a Hopf manifold with a flat holomorphic parabolic geometry modelled on that generalized flag manifold.