Compact complex homogeneous manifolds with large automorphism groups

Abstract

Let X be a compact complex homogeneous manifold and let Aut(X) be the complex Lie group of holomorphic automorphisms of X. It is well-known that the dimension of Aut(X) is bounded by an integer that depends only on n=dim X. Moreover, if X is Kahler then dimAut (X)≤n(n+2) with equality only when X is complex projective space. In this article examples of non-Kahler compact complex homogeneous manifolds X are given that demonstrate dimAut(X) can depend exponentially on n.