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Embedding of a Maximal Curve in a Hermitian Variety

Published online by Cambridge University Press:  04 December 2007

Gábor Korchmáros  and
Fernando Torres
Gábor Korchmáros
Affiliation:
Dipartimento di Matematica, Universitá della Basilicata, via N. Sauro 85, 85100 Potenza, Italy. E-mail: korchmaros@unibas.it
Fernando Torres
Affiliation:
IMECC-UNICAMP, Cx. P. 6065, Campinas-13083-970-SP, Brazil. E-mail: ftorres@ime.unicamp.br
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Abstract

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Let $\cal X$ be a projective, geometrically irreducible, non-singular, algebraic curve defined over a finite field Fq2 of order q2. If the number of Fq2-rational points of $\cal X$ satisfies the Hasse–Weil upper bound, then $\cal X$ is said to be Fq2-maximal. For a point P0 ∈ $\cal X$(Fq2), let π be the morphism arising from the linear series $\cal D$: = |(q + 1)P0|, and let N: = dim($\cal D$). It is known that N [ges ] 2 and that π is independent of P0 whenever $\cal X$ is Fq2-maximal.

Keywords

finite fieldmaximal curveHermitian varietylinear series
Type
Research Article
Information
Compositio Mathematica , Volume 128 , Issue 1 , August 2001 , pp. 95 - 113
Copyright
© 2001 Kluwer Academic Publishers