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arXiv · 2511.09380

Bott manifolds of Bott--Samelson type and assemblies of ordered partitions

Junho Jeong·Jang Soo Kim·Eunjeong Lee
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Abstract

A Bott manifold is a smooth projective toric variety having an iterated $\mathbb{C} P^1$-bundle structure. A certain family of Bott manifolds is used to understand the structure of Bott--Samelson varieties (or Bott--Samelson--Demazure--Hansen varieties), which provide desingularizations of Schubert varieties. Indeed, each Bott--Samelson variety is diffeomorphic to a Bott manifold. However, not all Bott manifolds originate from Bott--Samelson varieties. Those that do are specifically referred to as Bott manifolds of Bott--Samelson type. In this paper, we provide a characterization of Bott manifolds of Bott--Samelson type by exploring their relationship with combinatorial objects called assemblies of ordered partitions. Using this relationship, we enumerate Bott manifolds of Bott--Samelson type and describe isomorphic Bott manifolds of Bott--Samelson type in terms of assemblies of ordered partitions.

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Junho Jeong, Jang Soo Kim, Eunjeong Lee. 2025-11-12. Bott manifolds of Bott--Samelson type and assemblies of ordered partitions. https://arxiv.org/abs/2511.09380

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