The Hartogs extension problem for holomorphic parabolic and reductive geometries (Q331077)

The aim of this paper is to show that holomorphic parabolic geometries obey the Hartogs extension phenomenon, which constrains the possible singularities they can have. This fact is in contrast with many examples of holomorphic Cartan connections which do \textit{not} obey the Hartogs extension phenomenon. Also, the author provides new examples of holomorphic parabolic geometries on compact complex manifolds. Finally, the Hartogs extension is used to classify the Hopf manifolds which admit holomorphic reductive or holomorphic parabolic geometries.