Abstract
A real semisimple Lie group \(G_0\) embedded in its complexification G has only finitely many orbits in any G-flag manifold \(Z=G/Q\). The complex geometry of its open orbits D (flag domains) is studied from the point of view of compact complex submanifolds C (cycles) which arise as orbits of certain distinguished subgroups. Normal bundles E of the cycles are analyzed in some detail. It is shown that E is trivial if and only if D is holomorphically convex, in fact a product of C and a Hermitian symmetric space, and otherwise D is pseudoconcave. The proofs make use of basic results of Sommese and of Snow which are discussed in some detail.
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Dedicated to J. A. Wolf on the occasion of his 80th birthday. His fundamental work in the area of this paper has been a guiding light.
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Hong, J., Huckleberry, A. & Seo, A. Normal bundles of cycles in flag domains. São Paulo J. Math. Sci. 12, 278–289 (2018). https://doi.org/10.1007/s40863-018-0094-z
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DOI: https://doi.org/10.1007/s40863-018-0094-z