COMPACT COMPLEX HOMOGENEOUS MANIFOLDS WITH LARGE AUTOMORPHISM-GROUPS

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 onl y on n = dimX. Moreover, if X is Kahler then dim Aut (X) less than or equal to n(n + 2) with equality only when X is complex projective spac e. In this article examples of non-Kahler compact complex homogeneous manifolds X are given that demonstrate dim Aut(X) can depend exponenti ally on n.