Plane sections of Fermat surfaces over finite fields

H. Borges, G. Cook, M. Coutinho

In this paper, we characterize all curves over ${\mathbb{F}}_q$ arising from a plane section $$\mathcal{P}:X_3-e_0{X}_0-e_1{X}_1-e_2{X}_2=0$$ of the Fermat surface $$ \mathcal{S} : X…