On plane maximal curves

Details On plane maximal curves On plane maximal curves

1998-02-23

arxiv.org/abs/math/9802113v1

Compositio Math. 121(2) (2000), 163--181

Mathematics

Algebraic Geometry

18 pages, Latex2e

Scientific paper

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.

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