A bound on the number of points of a plane curve

DOI10.1016/j.ffa.2007.09.004zbMath1185.14017OpenAlexW1998774967MaRDI QIDQ2469467

Peter Sziklai

Publication date: 6 February 2008

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

Full work available at URL: https://doi.org/10.1016/j.ffa.2007.09.004

zbMATH Keywords

projective planeplane curve

Mathematics Subject Classification ID

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

Related Items (12)

On the constant 𝐷(𝑞) defined by Homma ⋮ Around Sziklai's conjecture on the number of points of a plane curve over a finite field ⋮ Small point sets of \(\text{PG}(n, q ^{3})\) intersecting each \(k\)-subspace in 1 mod \(q\) points ⋮ Fragments of plane filling curves of degree \(q + 2\) over the finite field of \(q\) elements, and of affine-plane filling curves of degree \(q + 1\) ⋮ Hypersurfaces achieving the Homma-Kim bound ⋮ 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 ⋮ Construction of rational surfaces yielding good codes ⋮ The characterization of Hermitian surfaces by the number of points ⋮ Toward determination of optimal plane curves with a fixed degree over a finite field ⋮ Sziklai's conjecture on the number of points of a plane curve over a finite field. III ⋮ An upper bound on the number of rational points of arbitrary projective varieties over finite fields

Cites Work

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• On (\(k,p^{e}\))-arcs in Desarguesian planes
• Elementary proofs of two fundamental theorems of B. Segre without using the Hasse-Weil theorem
• On the incompleteness of \((k,n)\)-arcs in Desarguesian planes of order \(q\) where \(n\) divides \(q\)
• On multiple nuclei and a conjecture of Lunelli and Sce

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