Minimal value set polynomials and a generalization of the Hermitian curve

2014/01/15 by Herivelto Borges, Borges, Herivelto, Ricardo Conceicão +1
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.1401.3713

arxiv created 2014/01/15 · arxiv updated 2014/01/16

Abstract

We use a recent characterization of minimal value set polynomials and q- Frobenius nonclassical curves to construct curves that generalize the Hermitian curve. The genus g and the number N of \mathbbF_q-rational points of the curves are computed and, for a special family of these curves, we determine the Weierstrass semigroup at the unique point at infinity. These special curves yield new examples of Castle curves and improve on a previous example of Garcia-Stichtenoth of curves with large ratio N/g.

Related

• Frobenius nonclassical components of curves with separated variables
• Triples of rational points on the Hermitian curve and their Weierstrass\n semigroups
• Minimal value set binomials and Frobenius nonclassical curves
• Relatives of the Hermitian curve
• Generalized Weierstrass semigroups at several points on certain maximal curves which cannot be covered by the Hermitian curve