Rational points on \(K3\) surfaces in \(\mathbb{P}^ 1\times\mathbb{P}^ 1\times\mathbb{P}^ 1\)

DOI10.1007/BF01444236zbMath0877.14017MaRDI QIDQ1923245

Arthur Baragar

Publication date: 10 December 1997

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/183002

zbMATH Keywords

rational pointsautomorphismsK3 surfacelogarithmic heightexponential heightnumber of points of bounded height

Mathematics Subject Classification ID

Rational points (14G05) (K3) surfaces and Enriques surfaces (14J28) Arithmetic varieties and schemes; Arakelov theory; heights (14G40) Automorphisms of surfaces and higher-dimensional varieties (14J50)

Related Items (12)

Automorphisms of surfaces in a class of Wehler \(K3\) surfaces with Picard number \(4\) ⋮ Canonical vector heights on K3 surfaces with Picard number three— An argument for nonexistence ⋮ Counting points of bounded height in monoid orbits ⋮ Canonical vector heights on \(K3\) surfaces -- a nonexistence result ⋮ The dynamical and arithmetical degrees for eigensystems of rational self-maps ⋮ Examples of dynamical degree equals arithmetic degree ⋮ Rational curves on K3 surfaces in ℙ¹×ℙ¹×ℙ¹ ⋮ On the dynamics of the automorphism group of \(K3\) surfaces ⋮ Conway topograph, -dynamics and two-valued groups ⋮ Orbit counting in polarized dynamical systems ⋮ Canonical heights, invariant currents, and dynamical eigensystems of morphisms for line bundles ⋮ Counting rational points on K3 surfaces

Cites Work

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• On a generalization of Markoff's theory.
• The Markoff equation \(X^ 2+Y^ 2+Z^ 2=aXYZ\) over quadratic imaginary fields
• Rational points of bounded height on Fano varieties
• On the number of rational points of bounded height on algebraic varieties
• Rational points on K3 surfaces: A new canonical height
• Number theory III: Diophantine geometry
• On Perrine's generalized Markoff equations
• Products of consecutive integers and the Markoff equation
• On the Number of Markoff Numbers Below a Given Bound
• Über die Diophantische Gleichung ax2 + by2 + cz2 = dxyz.
• The Apollonian Packing of Circles
• On the Integer Solutions of the Equation x ² +y ² +z ² +2xyz = n
• On products of consecutive integers

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