Hyperbolicity of cycle spaces and automorphism groups of flag domains

2010/03/31 by Alan Huckleberry, Huckleberry, Alan · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #math.AG #math.CV

paper · pdf · doi:10.48550/arxiv.1003.5974

arxiv created 2010/03/31 · openalex publication_date 2010/03/31 · arxiv updated 2010/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

If G₀ is a real form of a complex semisimple Lie group G and Z is compact G-homogeneous projective algebraic manifold, then G₀ has only finitely many orbits on Z. Complex analytic properties of open G₀-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 G₀.

Cited by

• Cycle Connectivity and Automorphism Groups of Flag Domains

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