9,139 research outputs found
On maximal curves
We study arithmetical and geometrical properties of maximal curves, that is,
curves defined over the finite field F_{q^2} whose number of F_{q^2}-rational
points reaches the Hasse-Weil upper bound. Under a hypothesis on non-gaps at a
rational point, we prove that maximal curves are F_{q^2}-isomorphic to y^q + y
= x^m, for some . As a consequence we show that a maximal curve of
genus g=(q-1)^2/4 is F_{q^2}-isomorphic to the curve y^q + y = x^{(q+1)/2}.Comment: LaTex2e, 17 pages; this article is an improved version of the paper
alg-geom/9603013 (by Fuhrmann and Torres
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