On Manin's conjecture for a certain singular cubic surface

DOI10.1016/j.ansens.2006.12.002zbMath1125.14008arXivmath/0509370OpenAlexW2131073910WikidataQ122976490 ScholiaQ122976490MaRDI QIDQ5297491

Régis de la Bretèche, Ulrich Derenthal, Timothy D. Browning

Publication date: 11 July 2007

Published in: Annales Scientifiques de l’École Normale Supérieure (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0509370

zbMATH Keywords

singular surfaceasymptotic formula

Mathematics Subject Classification ID

Rational points (14G05) Singularities of surfaces or higher-dimensional varieties (14J17) Varieties over global fields (11G35) Heights (11G50) Arithmetic ground fields for surfaces or higher-dimensional varieties (14J20) Global ground fields in algebraic geometry (14G25)

Related Items (21)

Computations with Algebraic Surfaces ⋮ Universal torsors of del Pezzo surfaces and homogeneous spaces ⋮ Computing Cox rings ⋮ Imaginary quadratic points on toric varieties via universal torsors ⋮ Quadratic congruences on average and rational points on cubic surfaces ⋮ Counting imaginary quadratic points via universal torsors ⋮ Examples of counting curves on surfaces ⋮ Singular del Pezzo surfaces that are equivariant compactifications ⋮ Geometric consistency of Manin's conjecture ⋮ A Zariski dense exceptional set in Manin's conjecture: dimension 2 ⋮ On the saturation number for singular cubic surfaces ⋮ Cox rings over nonclosed fields ⋮ Fonction zêta des hauteurs associée à une certaine surface cubique ⋮ On Manin's conjecture for singular del Pezzo surfaces of degree 4. I ⋮ Manin's conjecture for a cubic surface with 2A₂ + A₁ singularity type ⋮ Manin's conjecture for certain spherical threefolds ⋮ Height zeta functions ⋮ Algebraic points, non-anticanonical heights and the Severi problem on toric varieties ⋮ On exceptional sets in Manin's conjecture ⋮ Counting curves on the plane blown up in three collinear points ⋮ Cox rings of cubic surfaces and Fano threefolds

Cites Work

• Rational points of bounded height on Fano varieties
• On the distribution of points of bounded height on equivariant compactifications of vector groups.
• Heights and Tamagawa measures on Fano varieties
• On Manin's conjecture for singular del Pezzo surfaces of degree 4. I
• The density of rational points on a certain singular cubic surface
• The Estimation of Complete Exponential Sums
• Some extremal functions in Fourier analysis
• On the Classification of Cubic Surfaces
• Tamagawa numbers of polarized algebraic varieties
• The density of rational points on cubic surfaces
• On Manin's Conjecture for a Certain Singular Cubic Surface Over Imaginary Quadratic Fields
• On Manin's conjecture for singular del Pezzo surfaces of degree four, II
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