Blocking sets from a union of plane curves

Shamil Asgarli; Dragos Ghioca; Chi Hoi Yip

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arXiv · 2510.15332

Blocking sets from a union of plane curves

Shamil Asgarli·Dragos Ghioca·Chi Hoi Yip

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Abstract

Motivated by a question of Erd\H{o}s 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.

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BibTeX RIS

Shamil Asgarli, Dragos Ghioca, Chi Hoi Yip. 2025-10-17. Blocking sets from a union of plane curves. https://arxiv.org/abs/2510.15332

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