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

2019/06/01 by Homma, Masaaki
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1906.00164

Abstract

Nonsingular plane curves over a finite field \mathbbF_q of degree q+2 passing through all the \mathbbF_q-points of the plane admita representation by 3× 3 matrices over \mathbbF_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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