Hypersurfaces achieving the Homma-Kim bound

Andrea Luigi Tironi

Hypersurfaces achieving the Homma-Kim bound

Algebraic Geometry 2016-04-19 v3

Authors: Andrea Luigi Tironi

Abstract

Let $X$ be a hypersurface in $\mathbb{P}^N$ with $N\geq 3$ defined over a finite field. The main result of this note is the classification, up to projective equivalence, of hypersurfaces $X$ as above without a linear component when the number of their rational points achieves the Homma-Kim bound.

Keywords

hypersurfaces algebraic surfaces hyperbolic surfaces

Cite

@article{arxiv.1410.7320,
  title  = {Hypersurfaces achieving the Homma-Kim bound},
  author = {Andrea Luigi Tironi},
  journal= {arXiv preprint arXiv:1410.7320},
  year   = {2016}
}

Comments

14 pages; the final presentation of the main topics has been improved by some changes and additional results, and some mistakes and typos have been corrected

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