On plane maximal curves
Algebraic Geometry
2007-05-23 v1
Abstract
The genus of a maximal curve over a finite field with r^2 elements is either g_0=r(r-1)/2 or less than or equal to g_1=(r-1)^2/4. Maximal curves with genus g_0 or g_1 have been characterized up to isomorphism. A natural genus to be studied is g_2=(r-1)(r-3)/8, and for this genus there are two non-isomorphism maximal curves known when r \equiv 3 (mod 4). Here, a maximal curve with genus g_2 and a non-singular plane model is characterized as a Fermat curve of degree (r+1)/2.
Keywords
Cite
@article{arxiv.math/9802113,
title = {On plane maximal curves},
author = {A. Cossidente and J. W. P. Hirschfeld and G. Korchmaros and F. Torres},
journal= {arXiv preprint arXiv:math/9802113},
year = {2007}
}
Comments
18 pages, Latex2e