On maximal curves
alg-geom
2008-02-03 v1 Algebraic Geometry
Abstract
We study arithmetical and geometrical properties of maximal curves, that is, curves defined over the finite field F_{q^2} whose number of F_{q^2}-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_{q^2}-isomorphic to y^q + y = x^m, for some . As a consequence we show that a maximal curve of genus g=(q-1)^2/4 is F_{q^2}-isomorphic to the curve y^q + y = x^{(q+1)/2}.
Cite
@article{arxiv.alg-geom/9610023,
title = {On maximal curves},
author = {Rainer Fuhrmann and Arnaldo Garcia and Fernando Torres},
journal= {arXiv preprint arXiv:alg-geom/9610023},
year = {2008}
}
Comments
LaTex2e, 17 pages; this article is an improved version of the paper alg-geom/9603013 (by Fuhrmann and Torres)