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Projective plane curves over a finite field with conical components

Department of Mathematics, Faculty of Sciences University of Tabuk, 71491 Tabuk, Saudi Arabia KSA IPEI El-manar, University of Tunis El Manar, 1068 Tunis, Tunisia

* Corresponding Author
Annals of Communications in Mathematics 2023
, 6 (1),
67-71.
https://doi.org/10.62072/acm2023060107
Received: 28 Feb 2023 |
Accepted: 25 Mar 2023 |
Published: 31 Mar 2023

Abstract

We present the list of maximal projective plane curves containing conics and those which are arrangements of conics. The number of rational points and the corresponding polynomials are given. The third highest number of points of projective curves of degree d over a finite field Fq (d < [q/3]) is associated only to some linear curves. We show that for q/2 + 2 < d < q, this is no longer the case: the third highest number of points can also be obtained by some curves containing a conic. Throughout this work, we obtain some bounds concerning the number of Fq-points of curves with linear, conic and cubic factors. these bounds apply (not sharply) to irreducible curves

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Cite This Article

Projective plane curves over a finite field with conical components.

Annals of Communications in Mathematics,

2023,
6 (1):
67-71.
https://doi.org/10.62072/acm2023060107
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  • Copyright (c) 2023 by the Author(s). Licensee Techno Sky Publications. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

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