Binary Curves of small fixed genus and gonality with many rational points

Xander Faber; Jon Grantham

doi:10.1016/j.jalgebra.2022.01.008

Binary Curves of small fixed genus and gonality with many rational points

Number Theory 2022-08-09 v2

Authors: Xander Faber , Jon Grantham

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Abstract

We determine the maximum number of rational points on a curve over $\mathbb{F}_2$ with fixed gonality and small genus.

Keywords

rational points on curves algebraic curves rational maps

Cite

@article{arxiv.2005.07054,
  title  = {Binary Curves of small fixed genus and gonality with many rational points},
  author = {Xander Faber and Jon Grantham},
  journal= {arXiv preprint arXiv:2005.07054},
  year   = {2022}
}

Comments

This version differs from the published edition in one significant way: it contains an appendix on quadratic forms over finite fields (including characteristic 2) and their associated orthogonal groups

Binary Curves of small fixed genus and gonality with many rational points

Abstract

Keywords

Cite

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