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

zbMath1211.14037arXiv0907.1325MaRDI QIDQ3062278

Masaaki Homma, Seon Jeong Kim

Publication date: 3 January 2011

Full work available at URL: https://arxiv.org/abs/0907.1325

zbMATH Keywords

finite fieldsrational pointsplane curves

Mathematics Subject Classification ID

Rational points (14G05) Plane and space curves (14H50) Enumerative problems (combinatorial problems) in algebraic geometry (14N10) Finite ground fields in algebraic geometry (14G15)

Related Items (12)

On the constant 𝐷(𝑞) defined by Homma ⋮ 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 ⋮ 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 ⋮ Sziklai's conjecture on the number of points of a plane curve over a finite field. III ⋮ CHARACTERIZING HERMITIAN VARIETIES IN THREE- AND FOUR-DIMENSIONAL PROJECTIVE SPACES ⋮ Maximum number of \(\mathbb{F}_q\)-rational points on nonsingular threefolds in \(\mathbb{P}^4\)

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