Curves of every genus with many points, I: Abelian and toric families

Details Curves of every genus with many points, I: Abelian and toric families Curves of every genus with many points, I: Abelian and toric families

1999-12-09

arxiv.org/abs/math/9912069v2

J. Algebra 250, no. 1 (2002), 353--370

Mathematics

Algebraic Geometry

LaTeX, 20 pages

Scientific paper

Let N_q(g) denote the maximal number of F_q-rational points on any curve of genus g over the finite field F_q. Ihara (for square q) and Serre (for general q) proved that limsup_{g-->infinity} N_q(g)/g > 0 for any fixed q. In their proofs they constructed curves with many points in infinitely many genera; however, their sequences of genera are somewhat sparse. In this paper, we prove that lim_{g-->infinity} N_q(g) = infinity. More precisely, we use abelian covers of P^1 to prove that liminf_{g-->infinity} N_q(g)/(g/log g) > 0, and we use curves on toric surfaces to prove that liminf_{g-->infty} N_q(g)/g^{1/3} > 0; we also show that these results are the best possible that can be proved with these families of curves.

Affiliated with

Also associated with

No associations

Rating

Curves of every genus with many points, I: Abelian and toric families does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Curves of every genus with many points, I: Abelian and toric families, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Curves of every genus with many points, I: Abelian and toric families will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-411295