Bott manifolds of Bott--Samelson type and assemblies of ordered partitions
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908648347795456 |
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| author | Jeong, Junho Kim, Jang Soo Lee, Eunjeong |
| author_facet | Jeong, Junho Kim, Jang Soo Lee, Eunjeong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_09380 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bott manifolds of Bott--Samelson type and assemblies of ordered partitions Jeong, Junho Kim, Jang Soo Lee, Eunjeong Algebraic Geometry Combinatorics Primary: 14M25, 14M15, Secondary: 05A05, 05E14, 05A19 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. |
| title | Bott manifolds of Bott--Samelson type and assemblies of ordered partitions |
| topic | Algebraic Geometry Combinatorics Primary: 14M25, 14M15, Secondary: 05A05, 05E14, 05A19 |
| url | https://arxiv.org/abs/2511.09380 |