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arXiv · 1807.07311

Normal bundles of cycles in flag domains

Jaehyun Hong·Alan Huckleberry·Aeryeong Seo
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Abstract

A real semisimple Lie group G_0 embedded in its complexification G has only finitely many orbits in any G-fag 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.

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Jaehyun Hong, Alan Huckleberry, Aeryeong Seo. 2018-07-19. Normal bundles of cycles in flag domains. https://arxiv.org/abs/1807.07311

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