Numbers of points of surfaces in the projective $3$-space over finite fields

Masaaki Homma; Seon Jeong Kim

Numbers of points of surfaces in the projective $3$-space over finite fields

Algebraic Geometry 2014-09-23 v1

Authors: Masaaki Homma , Seon Jeong Kim

Abstract

In the previous paper, we established an elementary bound for numbers of points of surfaces in the projective $3$ -space over ${\Bbb F}_q$ . In this paper, we give the complete list of surfaces that attain the elementary bound. Precisely those surfaces are the hyperbolic surface, the nonsingular Hermitian surface, and the surface of minimum degree containing all ${\Bbb F}_q$ -points of the $3$ -space.

Keywords

projective space finite fields number of points algebraic surfaces hyperbolic surface Hermitian surface elementary bound

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@article{arxiv.1409.5842,
  title  = {Numbers of points of surfaces in the projective $3$-space over finite fields},
  author = {Masaaki Homma and Seon Jeong Kim},
  journal= {arXiv preprint arXiv:1409.5842},
  year   = {2014}
}

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8 pages

Numbers of points of surfaces in the projective $3$-space over finite fields

Abstract

Keywords

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