On maximal curves

1996/10/31 by Fuhrmann, Rainer, Garcia, Arnaldo, Torres, Fernando · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.alg-geom/9610023

Abstract

We study arithmetical and geometrical properties of maximal curves, that is, curves defined over the finite field F_q² whose number of F_q²-rational points reaches the Hasse-Weil upper bound. Under a hypothesis on non-gaps at a rational point, we prove that maximal curves are F_q²-isomorphic to y^q + y = x^m, for some m ∈ Z⁺. As a consequence we show that a maximal curve of genus g=(q-1)²/4 is F_q²-isomorphic to the curve y^q + y = x^(q+1)/2.

Cited by

• The automorphism groups of a maximal function field with the second largest genus and its algebraic geometry codes
• Uniqueness of Skabelund Maximal Curves via Genus and Automorphism Groups

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