Triangular arrangements on the projective plane
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2019
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| Acceso en línea: | |
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| _version_ | 1866911592321384448 |
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| author | Marchesi, Simone Vallès, Jean |
| author_facet | Marchesi, Simone Vallès, Jean |
| contents | In this work we study line arrangements consisting in lines passing through three non-aligned points. We call them triangular arrangements. We prove that any combinatorics of a triangular arrangement is always realized by a Roots-of-Unity-Arrangement, which is a particular class of triangular arrangements. Among these Roots-of Unity-Arrangements, we provide conditions that ensure their freeness. Finally, we give two triangular arrangements having the same weak combinatorics, such that one is free but the other one is not. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1903_08885 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Triangular arrangements on the projective plane Marchesi, Simone Vallès, Jean Algebraic Geometry Algebraic Topology Combinatorics 52C35, 14F06, 32S22 In this work we study line arrangements consisting in lines passing through three non-aligned points. We call them triangular arrangements. We prove that any combinatorics of a triangular arrangement is always realized by a Roots-of-Unity-Arrangement, which is a particular class of triangular arrangements. Among these Roots-of Unity-Arrangements, we provide conditions that ensure their freeness. Finally, we give two triangular arrangements having the same weak combinatorics, such that one is free but the other one is not. |
| title | Triangular arrangements on the projective plane |
| topic | Algebraic Geometry Algebraic Topology Combinatorics 52C35, 14F06, 32S22 |
| url | https://arxiv.org/abs/1903.08885 |