Blocking sets from a union of plane curves
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908599229349888 |
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| author | Asgarli, Shamil Ghioca, Dragos Yip, Chi Hoi |
| author_facet | Asgarli, Shamil Ghioca, Dragos Yip, Chi Hoi |
| contents | Motivated by a question of Erdős on blocking sets in a projective plane that intersect every line only a few times, several authors have used unions of algebraic curves to construct such sets in $\mathbb{P}^2(\mathbb{F}_q)$. In this paper, we provide new constructions of blocking sets in $\mathbb{P}^2(\mathbb{F}_q)$ from a union of geometrically irreducible curves of a fixed degree $d$. We also establish lower bounds on the number of such curves required to form a blocking set. Our proofs combine tools from arithmetic geometry and combinatorics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_15332 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Blocking sets from a union of plane curves Asgarli, Shamil Ghioca, Dragos Yip, Chi Hoi Algebraic Geometry Combinatorics Number Theory Primary: 14N05, 51E21, Secondary: 14C21, 14H50, 14G15 Motivated by a question of Erdős on blocking sets in a projective plane that intersect every line only a few times, several authors have used unions of algebraic curves to construct such sets in $\mathbb{P}^2(\mathbb{F}_q)$. In this paper, we provide new constructions of blocking sets in $\mathbb{P}^2(\mathbb{F}_q)$ from a union of geometrically irreducible curves of a fixed degree $d$. We also establish lower bounds on the number of such curves required to form a blocking set. Our proofs combine tools from arithmetic geometry and combinatorics. |
| title | Blocking sets from a union of plane curves |
| topic | Algebraic Geometry Combinatorics Number Theory Primary: 14N05, 51E21, Secondary: 14C21, 14H50, 14G15 |
| url | https://arxiv.org/abs/2510.15332 |