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

Shintarô Kuroki; Eunjeong Lee; Jongbaek Song; Dong Youp Suh

doi:10.2140/pjm.2020.308.347

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arXiv · 1708.02082

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

Shintarô Kuroki·Eunjeong Lee·Jongbaek Song·Dong Youp Suh

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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.

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BibTeX RIS

Shintarô Kuroki, Eunjeong Lee, Jongbaek Song, Dong Youp Suh. 2017-08-07. Flag Bott manifolds and the toric closure of a generic orbit associated to a generalized Bott manifold. https://doi.org/10.2140/pjm.2020.308.347

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