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

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 $q+1$.

17 pages; a revised version

References in corpus (1)

• Curves containing all points of a finite projective Galois plane