Embedding of a Maximal Curve in a Hermitian Variety

Let 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 X satisfies the Hasse–Weil upper bound, then X is said to be Fq2-maximal. For a point P0 ∈ X(Fq2), let π be the morphism arising from the linear series D: = |(q + 1)P0|, and let N: = dim(D). It is known that N ≥ 2 and that π is independent of P0 whenever X is Fq2-maximal.

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