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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 |
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Vol. 308 (2020), No. 2, 347–392
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Abstract |
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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. |
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Keywords
flag Bott tower, flag Bott manifold, generalized Bott
manifold, GKM theory, toric manifold, blow-up
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Mathematical Subject Classification 2010
Primary: 14M15, 55R10
Secondary: 14M25, 57S25
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Milestones
Received: 6 November 2018
Revised: 15 September 2019
Accepted: 6 June 2020
Published: 9 December 2020
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Authors |
| Shintarô Kuroki | |
| Department of Applied
Mathematics Okayama University of Science Okayama-shi Okayama Japan |
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| Eunjeong Lee | |
| Center for Geometry and
Physics Institute for Basic Science Pohang Republic of Korea |
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| Jongbaek Song | |
| School of Mathematics KIAS Seoul Republic of Korea |
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| Dong Youp Suh | |
| Department of Mathematical
Sciences KAIST Daejeon Republic of Korea |
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