Manin's conjecture for a cubic surface with D_5 singularity
T. D. Browning, U. Derenthal
TL;DR
This paper proves Manin's conjecture for a specific class of singular cubic surfaces with D_5 singularities, advancing understanding of rational points distribution on algebraic varieties.
Contribution
It provides the first proof of Manin's conjecture for a split singular cubic surface with D_5 singularity.
Findings
Manin's conjecture is confirmed for the D_5 singular cubic surface.
The distribution of rational points aligns with predicted asymptotic formulas.
The methods developed may apply to other singular algebraic surfaces.
Abstract
The Manin conjecture is established for a split singular cubic surface in P^3, with singularity type D_5.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Algebraic Geometry and Number Theory · Geometric and Algebraic Topology