1998/02/23 by A. Cossidente, J. W. P. Hirschfeld, G. Korchmaros +1
Mathematics · #math.AG #msc:11G20 #msc:11G #msc:11 #msc:14G15 #msc:14G #msc:14
published as Compositio Math. 121(2) (2000), 163--181 · 18 pages, Latex2e
arxiv created 1998/02/23 · arxiv updated 2009/11/30
The genus of a maximal curve over a finite field with r2 elements is either g0=r(r-1)/2 or less than or equal to g1=(r-1)2/4. Maximal curves with genus g0 or g1 have been characterized up to isomorphism. A natural genus to be studied is g2=(r-1)(r-3)/8, and for this genus there are two non-isomorphism maximal curves known when r ≡ 3 (mod 4). Here, a maximal curve with genus g2 and a non-singular plane model is characterized as a Fermat curve of degree (r+1)/2.