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arXiv · 2301.06019

Proportion of blocking curves in a pencil

Shamil Asgarli·Dragos Ghioca·Chi Hoi Yip
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Abstract

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.

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Shamil Asgarli, Dragos Ghioca, Chi Hoi Yip. 2023-01-15. Proportion of blocking curves in a pencil. https://doi.org/10.1016/j.disc.2025.114668

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