On maximal curves in characteristic two
Abstract
The genus g of an F_{q^2}-maximal curve satisfies g=g_1:=q(q-1)/2 or g\le g_2:= [(q-1)^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 non-gap at some point of the curve.
- Publication:
-
arXiv Mathematics e-prints
- 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
- E-Print:
- 14 pages, LaTex2e