Manin's conjecture for a quartic del Pezzo surface with \(A_{4}\) singularity

DOI10.5802/aif.2462zbMath1193.14028arXiv0710.1560OpenAlexW2964016655WikidataQ122905867 ScholiaQ122905867MaRDI QIDQ2390097

Ulrich Derenthal, Timothy D. Browning

Publication date: 20 July 2009

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0710.1560

zbMATH Keywords

Manin's conjecturerational pointsdel Pezzo surfacesDiophantine equations

Mathematics Subject Classification ID

Rational points (14G05) Counting solutions of Diophantine equations (11D45) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Varieties over global fields (11G35) Arithmetic ground fields for surfaces or higher-dimensional varieties (14J20) Global ground fields in algebraic geometry (14G25)

Related Items (8)

Counting imaginary quadratic points via universal torsors ⋮ Examples of counting curves on surfaces ⋮ Singular del Pezzo surfaces that are equivariant compactifications ⋮ Volumes of Zariski chambers ⋮ Manin's conjecture for a cubic surface with 2A₂ + A₁ singularity type ⋮ Counting imaginary quadratic points via universal torsors, II ⋮ Manin's conjecture for a quartic del Pezzo surface with \(\mathbb A_3\) singularity and four lines ⋮ THE POWER‐SAVING MANIN–PEYRE CONJECTURE FOR A SENARY CUBIC

Cites Work

• The nef cone volume of generalized del Pezzo surfaces
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• On the distribution of points of bounded height on equivariant compactifications of vector groups.
• Heights and Tamagawa measures on Fano varieties
• On a constant arising in Manin's conjecture for del Pezzo surfaces
• On Manin's conjecture for singular del Pezzo surfaces of degree 4. I
• Arithmetic on Singular Del Pezzo Surfaces
• Manin's conjecture for toric varieties
• Singular del Pezzo surfaces whose universal torsors are hypersurfaces
• UNIVERSAL TORSORS OVER DEL PEZZO SURFACES AND RATIONAL POINTS
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