Vol. 308, No. 2, 2020

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Flag Bott manifolds and the toric closure of a generic orbit associated to a generalized Bott manifold

Shintarô Kuroki, Eunjeong Lee, Jongbaek Song and Dong Youp Suh

Vol. 308 (2020), No. 2, 347–392
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.

Keywords
flag Bott tower, flag Bott manifold, generalized Bott manifold, GKM theory, toric manifold, blow-up
Mathematical Subject Classification 2010
Primary: 14M15, 55R10
Secondary: 14M25, 57S25
Milestones
Received: 6 November 2018
Revised: 15 September 2019
Accepted: 6 June 2020
Published: 9 December 2020
Authors
Shintarô Kuroki
Department of Applied Mathematics
Okayama University of Science
Okayama-shi
Okayama
Japan
Eunjeong Lee
Center for Geometry and Physics
Institute for Basic Science
Pohang
Republic of Korea
Jongbaek Song
School of Mathematics
KIAS
Seoul
Republic of Korea
Dong Youp Suh
Department of Mathematical Sciences
KAIST
Daejeon
Republic of Korea