Points on singular Frobenius nonclassical curves

Herivelto Borges; Masaaki Homma

Points on singular Frobenius nonclassical curves

Algebraic Geometry 2015-11-03 v1

Authors: Herivelto Borges , Masaaki Homma

Abstract

In 1990, Hefez and Voloch proved that the number of $F_q$ -rational points on a nonsingular plane $q$ -Frobenius nonclassical curve of degree $d$ is $N = d(q-d+2)$ . We address these curves in the singular setting. In particular, we prove that $d(q-d + 2)$ is a lower bound on the number of $F_q$ -rational points on such curves of degree $d$ .

Keywords

rational points on curves

Cite

@article{arxiv.1511.00339,
  title  = {Points on singular Frobenius nonclassical curves},
  author = {Herivelto Borges and Masaaki Homma},
  journal= {arXiv preprint arXiv:1511.00339},
  year   = {2015}
}

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