On maximal curves in characteristic two
Abstract
The genus g of an F_{q^2}maximal curve satisfies g=g_1:=q(q1)/2 or g\le g_2:= [(q1)^2/4]. Previously, such curves with g=g_1 or g=g_2, q odd, have been characterized up to isomorphism. Here it is shown that an F_{q^2}maximal curve with genus g_2, q even, is F_{q^2}isomorphic to the nonsingular model of the plane curve \sum_{i=1}^{t}y^{q/2^i}=x^{q+1}, q=2^t, provided that q/2 is a Weierstrass nongap at some point of the curve.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 November 1998
 DOI:
 10.48550/arXiv.math/9811091
 arXiv:
 arXiv:math/9811091
 Bibcode:
 1998math.....11091A
 Keywords:

 Algebraic Geometry;
 PC: 11G20;
 11G;
 11;
 SC: 14G15;
 14G;
 14
 EPrint:
 14 pages, LaTex2e