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arXiv · 2203.11595

Filling curves for $\mathbb{P}^1 \times \mathbb{P}^1$

Masaaki Homma·Seon Jeong Kim
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Abstract

We determine the minimal bi-degree(s) of an irreducible filling curve over $\mathbb{F}_q$ for $\mathbb{P}^1\times \mathbb{P}^1$. It is $(q+1, q+1)$ if $q\neq 2$, and they are $(4,3)$ and $(3,4)$ if $q=2$.

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Masaaki Homma, Seon Jeong Kim. 2022-03-22. Filling curves for $\mathbb{P}^1 \times \mathbb{P}^1$. https://arxiv.org/abs/2203.11595

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