Ampleness of Normal Bundles of Base Cycles in Flag Domains

Abstract

Flag domains are open orbits of noncompact real forms of complex semisimple Lie groups acting on flag manifolds. To each flag domain one can associate a compact complex manifold called the base cycle. The ampleness of the normal bundle of the base cycle in a flag domain measures the concavity near the base cycle. In this paper we compute the ampleness of normal bundles of base cycles in flag domains in various cases, including flag domains in the full flag manifolds G/B when G is classical, and period domains parameterizing polarized Hodge structures with fixed Hodge numbers.