On combinatorics of plus-one generated line arrangements
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915555925032960 |
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| author | Bromboszcz, Artur |
| author_facet | Bromboszcz, Artur |
| contents | In this note we focus on combinatorial aspects of plus-one generated line arrangements. We provide combinatorial constraints on such arrangements and we construct a polynomial that decodes the plus-one generated property. We present new examples of plus-one generated arrangements constructed by using classical Klein and Wiman reflection arrangements, and we detect, among all known sporadic simplicial arrangements up to $27$ lines, exactly $9$ arrangements that are minimal plus-one generated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_17317 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On combinatorics of plus-one generated line arrangements Bromboszcz, Artur Algebraic Geometry Combinatorics 14N20, 32S22, 14C20 In this note we focus on combinatorial aspects of plus-one generated line arrangements. We provide combinatorial constraints on such arrangements and we construct a polynomial that decodes the plus-one generated property. We present new examples of plus-one generated arrangements constructed by using classical Klein and Wiman reflection arrangements, and we detect, among all known sporadic simplicial arrangements up to $27$ lines, exactly $9$ arrangements that are minimal plus-one generated. |
| title | On combinatorics of plus-one generated line arrangements |
| topic | Algebraic Geometry Combinatorics 14N20, 32S22, 14C20 |
| url | https://arxiv.org/abs/2411.17317 |