Around Sziklai's conjecture on the number of points of a plane curve over a finite field

DOI10.1016/j.ffa.2009.02.008zbMath1194.14031OpenAlexW1966931331WikidataQ123352873 ScholiaQ123352873MaRDI QIDQ841239

Seon Jeong Kim, Masaaki Homma

Publication date: 15 September 2009

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ffa.2009.02.008

zbMATH Keywords

plane curvesboundmany points

Mathematics Subject Classification ID

Rational points (14G05) Arithmetic ground fields for curves (14H25) Finite ground fields in algebraic geometry (14G15)

Related Items (18)

On the constant 𝐷(𝑞) defined by Homma ⋮ Bounds for the number of points on curves over finite fields ⋮ On a number of rational points on a plane curve of low degree ⋮ Hypersurfaces achieving the Homma-Kim bound ⋮ The second largest number of points on plane curves over finite fields ⋮ The uniqueness of a plane curve of degree \(q\) attaining Sziklai's bound over \(\mathbb F_{q}\) ⋮ Optimal plane curves of degree \(q - 1\) over a finite field ⋮ Codes coming from a blowing up of the plane ⋮ Curves in a hyperbolic quadric surface with a large number of \({\mathbb{F}_{q}}\)-points ⋮ Numbers of points of surfaces in the projective 3-space over finite fields ⋮ The characterization of Hermitian surfaces by the number of points ⋮ Toward determination of optimal plane curves with a fixed degree over a finite field ⋮ On the number of Galois points for a plane curve in positive characteristic. III ⋮ Sziklai's conjecture on the number of points of a plane curve over a finite field. III ⋮ On non-singular Hermitian varieties of \(\mathrm{PG}(4, q^2)\) ⋮ CHARACTERIZING HERMITIAN VARIETIES IN THREE- AND FOUR-DIMENSIONAL PROJECTIVE SPACES ⋮ Maximum number of \(\mathbb{F}_q\)-rational points on nonsingular threefolds in \(\mathbb{P}^4\) ⋮ On Hermitian varieties in PG(6, q^2)

Uses Software

• manYPoints

Cites Work

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• Le geometrie di Galois
• Curves of genus 3 over small finite fields
• Nonsingular plane filling curves of minimum degree over a finite field and their automorphism groups: Supplements to a work of Tallini
• A bound on the number of points of a plane curve
• Quadratic forms, generalized Hamming weights of codes and curves with many points

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