Plane-filling curves of small degree over finite fields

2023/07/06 by Asgarli, Shamil, Ghioca, Dragos · 1 citation
#14G05 #14H50 #Algebraic Geometry (math.AG) #FOS: Mathematics #Primary: 14G15 #Secondary: 11G20

paper · doi:10.48550/arxiv.2307.03072

Abstract

A plane curve C in ℙ² defined over \mathbbF_q is called plane-filling if C contains every \mathbbF_q-point of ℙ². Homma and Kim, building on the work of Tallini, proved that the minimum degree of a smooth plane-filling curve is q+2. We study smooth plane-filling curves of degree q+3 and higher.

Cited by

• Minimal algebraic space filling curves on the product of projective lines

Related

• Tangent-filling plane curves over finite fields
• Nonsingular plane filling curves of minimum degree over a finite field and their automorphism groups: Supplements to a work of Tallini
• On algebraic space filling curves
• Points of Low Degree on Smooth Plane Curves
• Filling curves for ℙ¹ × ℙ¹