Line arrangements with many triple points
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909617165959168 |
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| author | Kühne, Lukas Szemberg, Tomasz Tutaj-Gasińska, Halszka |
| author_facet | Kühne, Lukas Szemberg, Tomasz Tutaj-Gasińska, Halszka |
| contents | In this paper, we construct an infinite series of line arrangements in characteristic two, each featuring only triple intersection points. This finding challenges the existing conjecture that suggests the existence of only a finite number of such arrangements, regardless of the characteristic. Leveraging the theory of matroids and employing computer algebra software, we rigorously examine the existence and non-existence across various characteristics of line arrangements with up to 19 lines maximizing the number of triple intersection points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14766 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Line arrangements with many triple points Kühne, Lukas Szemberg, Tomasz Tutaj-Gasińska, Halszka Combinatorics Algebraic Geometry 05B35, 14N20, 52C30 In this paper, we construct an infinite series of line arrangements in characteristic two, each featuring only triple intersection points. This finding challenges the existing conjecture that suggests the existence of only a finite number of such arrangements, regardless of the characteristic. Leveraging the theory of matroids and employing computer algebra software, we rigorously examine the existence and non-existence across various characteristics of line arrangements with up to 19 lines maximizing the number of triple intersection points. |
| title | Line arrangements with many triple points |
| topic | Combinatorics Algebraic Geometry 05B35, 14N20, 52C30 |
| url | https://arxiv.org/abs/2401.14766 |