FLAG BOTT MANIFOLDS AND THE TORIC CLOSURE OF A GENERIC ORBIT ASSOCIATED TO A GENERALIZED BOTT MANIFOLD

Abstract

To a direct sum of holomorphic line bundles, we can associate two librations, whose fibers are, respectively, the corresponding full flag manifold and the corresponding projective space. Iterating these procedures gives, respectively, a flag Bolt tower and a generalized Bott tower. It is known that a generalized Bolt tower is a toric manifold. However a flag Bolt tower is not toric in general but we show that it is a GKl'I manifold, and we also show that for a given generalized Bott tower we can find the associated flag Bott tower so that the closure of a generic torus orbit in the latter is a blow-up of the former along certain invariant submanifi olds. We use GKM theory together with toric geometric arguments.