Classification of all Galois subcovers of the Skabelund maximal curves

2021/04/29 by Peter Beelen, Beelen, Peter, Leonardo Landi +3
Engineering · Mathematics · Computer Science · #Advanced Numerical Analysis Techniques #Algebraic Geometry and Number Theory #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2104.14247

Abstract

In 2017 Skabelund constructed two new examples of maximal curves S_q and R_q as covers of the Suzuki and Ree curves, respectively. The resulting Skabelund curves are analogous to the Giulietti-Korchmáros cover of the Hermitian curve. In this paper a complete characterization of all Galois subcovers of the Skabelund curves S_q and R_q is given. Calculating the genera of the corresponding curves, we find new additions to the list of known genera of maximal curves over finite fields.

Related

• On some Galois covers of the Suzuki and Ree curves
• Some Ree and Suzuki curves are not Galois covered by the Hermitian curve
• Maximal curves from subcovers of the GK-curve
• Uniqueness of Skabelund Maximal Curves via Genus and Automorphism Groups
• On curves covered by the Hermitian curve, II