2000/03/28 by Angela Aguglia, Gabor Korchmaros, Fernando Torres
Mathematics · #math.AG #msc:11G20 #msc:11G #msc:11 #msc:14G15 #msc:14G #msc:14
published as Acta Arith. 98(2) (2001), 165--179 · 14 pages, LaTex2e
arxiv created 2000/03/28 · arxiv updated 2009/11/30
Some new results on plane Fq2-maximal curves are stated and proved. It is known that the degree d of such curves is upper bounded by q+1 and that d=q+1 if and only if the curve is Fq2-isomorphic to the Hermitian. We show that d≤ q+1 can be improved to d≤ (q+2)/2 apart from the case d=q+1 or q≤ 5. This upper bound turns out to be sharp for q odd. We also study the maximality of Hurwitz curves of degree n+1. We show that they are Fq2-maximal if and only if (q+1) divides (n2-n+1). Such a criterion is extended to a wider family of curves.