Hyperbolicity of cycle spaces and automorphism groups of flag domains
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Publication:4917532
DOI10.1353/AJM.2013.0016zbMATH Open1276.32016arXiv1003.5974OpenAlexW2031090877MaRDI QIDQ4917532
Publication date: 30 April 2013
Published in: American Journal of Mathematics (Search for Journal in Brave)
Abstract: If G_0 is a real form of a complex semisimple Lie group G and Z is compact G-homogeneous projective algebraic manifold, then G_0 has only finitely many orbits on Z. Complex analytic properties of open G_0-orbits D (flag domains) are studied. Schubert incidence-geometry is used to prove the Kobayashi hyperbolicity of certain cycle space components C_q(D). Using the hyperbolicity of C_q(D) and analyzing the action of Aut(D) on it, an exact description of Aut(D) is given. It is shown that, except in the easily understood case where D is holomorphically convex with a nontrivial Remmert reduction, it is a Lie group acting smoothly as a group of holomorphic transformations on D. With very few exceptions it is just G_0.
Full work available at URL: https://arxiv.org/abs/1003.5974
Semisimple Lie groups and their representations (22E46) Complex Lie groups, group actions on complex spaces (32M05) Homogeneous complex manifolds (32M10)
Related Items (5)
Cycle spaces of flag domains on Grassmannians and rigidity of holomorphic mappings ⋮ The Strommer-cyclids of the flag space ⋮ Automorphism groups of ind-varieties of generalized flags ⋮ Characterization of cycle domains via Kobayashi hyperbolicity ⋮ Cycle spaces of flag domains. A complex geometric viewpoint
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