Generic 1-connectivity of flag domains in Hermitian symmetric spaces

Cycle connectivity and pseudoconcavity of flag domains

We prove that a non-classical flag domain is pseudoconcave if it satisfies a certain condition on the root system. Moreover, we prove that every point in a one-codimensional real boundary orbit of a non-classical period domains is a pseudoconcave boundary point if it satisfies a certain Hodge-theoretical condition.

On deformations of flag manifolds with B2=1

Why withdrawn: Main theorem can only be proved, if the flag manifold F with b2=1 is additionally hermitian symmetric.Mistake made at the following place: If F is not hermitian symmetric, certain vector fields are not left invariant

Cycle Connectivity and Automorphism Groups of Flag Domains

A flag domain $D$ is an open orbit of a real form $G_0$ in a flag manifold $Z=G/P$ of its complexification. If $D$ is holomorphically convex, then, since it is a product of a Hermitian symmetric space of bounded type and a compact flag manifold, ${Aut}(D)$ is easily described. If $D$ is not holomorphically convex, then in our previous work (American J. Math, 136, Nr.2 (2013) 291-310 (arXiv: 1003.5974)) it was shown that ${Aut}(D)$ is a Lie group whose connected component at the identity agrees with $G_0$ except possibly in situations which arise in Onishchik's list of flag manifolds where ${Au…

Pseudoconcavity of flag domains: The method of supporting cycles

A flag domain of a real from $G_0$ of a complex semismiple Lie group $G$ is an open $G_0$-orbit $D$ in a (compact) $G$-flag manifold. In the usual way one reduces to the case where $G_0$ is simple. It is known that if $D$ possesses non-constant holomorphic functions, then it is the product of a compact flag manifold and a Hermitian symmetric bounded domain. This pseudoconvex case is rare in the geography of flag domains. Here it is shown that otherwise, i.e., when $\mathcal{O}(D)\cong\mathbb{C}$, the flag domain $D$ is pseudoconcave. In a rather general setting the degree of the pseudoconcavit…

$G^\mathbb C$ -旗流形中G-轨道的圈空间

Cycle spaces of G-orbits in $G^\mathbb C$-flag manifolds

证明了非厄米实型G的任意轨道在其复化的旗流形$Z=G^\mathbb C/Q$中的循环空间自然等价于只依赖于G的某个泛域.这使得使用复杂的几何方法，最近开发的目的是处理的情况下，开放的轨道，更好地了解连接到舒伯特品种和相关的复杂切片沿低维Gorbits。

Normal bundles of cycles in flag domains

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.