Minimal value set binomials and Frobenius nonclassical curves

2025/08/22 by Aprigio, Tiago, Guardieiro, João Paulo
#11C08 (Primary) 14Hxx (Secondary) #14H45 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2508.16541

Abstract

In this paper, we characterize all minimal value set binomials over \mathbbF_q, that is, binomials whose size of the set of images is the smallest possible. With this information, we also classify all quadrinomial curves with separated variables that are \mathbbF_q-Frobenius nonclassical for the morphism of lines.

Citations

• Points on singular Frobenius nonclassical curves
• Zeta functions of trinomial curves and maximal curves
• Frobenius nonclassical components of curves with separated variables
• On the characterization of minimal value set polynomials

Related

• Frobenius nonclassical components of curves with separated variables
• Minimal value set polynomials and a generalization of the Hermitian curve
• Frobenius nonclassicality with respect to linear systems of curves of arbitrary degree
• Duality for certain multi-Frobenius nonclassical curves in higher dimensional spaces
• Frobenius nonclassicality of Fermat curves with respect to cubics