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A bound on the number of points of a curve in projective space over a finite field

Published 25 Aug 2011 in math.AG | (1108.4975v1)

Abstract: For a nondegenerate irreducible curve $C$ of degree $d$ in ${\Bbb P}r$ over ${\Bbb F}_q$ with $r \geq 3$, we prove that the number $N_q(C)$ of ${\Bbb F}_q$-points of $C$ satisfies the inequality $N_q(C) \leq (d-1)q +1$, which is known as Sziklai's bound if $r=2$.

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Authors (1)

  1. Masaaki Homma 

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