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arXiv · 1906.00164

Fragments of plane filling curves of degree $q+2$ over the finite field of $q$ elements, and of affine-plane filling curves of degree $q+1$

Masaaki Homma
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Abstract

Nonsingular plane curves over a finite field $\mathbb{F}_q$ of degree $q+2$ passing through all the $\mathbb{F}_q$-points of the plane admita representation by $3\times 3$ matrices over $\mathbb{F}_q$. We classify their degenerations by means of the matrix representation, and also discuss the similar problem for the affine-plane filling curves of degree $q+1$.

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Masaaki Homma. 2019-06-01. Fragments of plane filling curves of degree $q+2$ over the finite field of $q$ elements, and of affine-plane filling curves of degree $q+1$. https://arxiv.org/abs/1906.00164

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