Proportion of blocking curves in a pencil
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866908432537223168 |
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| author | Asgarli, Shamil Ghioca, Dragos Yip, Chi Hoi |
| author_facet | Asgarli, Shamil Ghioca, Dragos Yip, Chi Hoi |
| contents | Let $\mathcal{L}$ be a pencil of plane curves defined over $\mathbb{F}_q$ with no $\mathbb{F}_q$-points in its base locus. We investigate the number of curves in $\mathcal{L}$ whose $\mathbb{F}_q$-points form a blocking set. When the degree of the pencil is allowed to grow with respect to $q$, we show that the geometric problem can be translated into a purely combinatorial problem about disjoint blocking sets. We also study the same problem when the degree of the pencil is fixed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_06019 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Proportion of blocking curves in a pencil Asgarli, Shamil Ghioca, Dragos Yip, Chi Hoi Algebraic Geometry Combinatorics Primary: 14H50, 51E21, Secondary: 14C21, 14N05, 14G15, 51E20 Let $\mathcal{L}$ be a pencil of plane curves defined over $\mathbb{F}_q$ with no $\mathbb{F}_q$-points in its base locus. We investigate the number of curves in $\mathcal{L}$ whose $\mathbb{F}_q$-points form a blocking set. When the degree of the pencil is allowed to grow with respect to $q$, we show that the geometric problem can be translated into a purely combinatorial problem about disjoint blocking sets. We also study the same problem when the degree of the pencil is fixed. |
| title | Proportion of blocking curves in a pencil |
| topic | Algebraic Geometry Combinatorics Primary: 14H50, 51E21, Secondary: 14C21, 14N05, 14G15, 51E20 |
| url | https://arxiv.org/abs/2301.06019 |