an:07191053
Zbl 1439.14082
Homma, Masaaki
Fragments of plane filling curves of degree \(q + 2\) over the finite field of \(q\) elements, and of affine-plane filling curves of degree \(q + 1\)
EN
Linear Algebra Appl. 589, 9-27 (2020).
00448515
2020
j
14G15 14H50 14G05 11G20
plane curve; finite field; rational point
Summary: 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 admit a representation by \(3 \times 3\) matrices over \(\mathbb{F}_q\). We classify their degenerations by means of the matrix representation. We also discuss the similar problem for the affine-plane filling projective curves of degree \(q + 1\).