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 fibrations, whose fibers are, respectively, the corresponding full flag manifold and the corresponding projective space. Iterating these procedures gives, respectively, a flag Bott tower and a generalized Bott tower. It is known that a generalized Bott tower is a toric manifold. However a flag Bott tower is not toric in general but we show that it is a GKM 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 submanifolds. We use GKM theory together with toric geometric arguments.

References in corpus (4)

• Generic torus orbit closures in Schubert varieties
• Toric Bruhat interval polytopes
• Flag Bott manifolds of general Lie type and their equivariant cohomology rings
• Algebraic and geometric properties of flag Bott-Samelson varieties and applications to representations

Cited by in corpus (6)

• Flag Bott manifolds of general Lie type and their equivariant cohomology rings
• Algebraic and geometric properties of flag Bott-Samelson varieties and applications to representations
• On Schubert varieties of complexity one
• Equivariant $K$-theory of flag Bott manifolds of general Lie type
• $K$-theory of Flag Bott manifolds
• Generic torus orbit closures in flag Bott manifolds