On Manin's conjecture for a certain singular cubic surface

By Ulrich Derenthal, Christopher Frei. 2005

65 citations recorded by the source corpus.

This paper contains a proof of the Manin conjecture for the singular cubic surface S⊂P3 that is defined by the equation x1x22+x2x02+x33=0. In fact if U⊂S is the Zariski open subset obtained by deleting the unique line from S, and H is the usual exponential height on P3(Q), then the height zeta function ∑x∈U(Q)H(x)−s is analytically continued to the half-plane Re(s)>9/10.

View Paper: https://www.semanticscholar.org/paper/26a9a2ffad6d41b1fd3253b2c2b22bb018f0511e

Citations in the corpus

• An overview of Manin's conjecture for del Pezzo surfaces (2005, background): “ line from S 7, and recall the notation (1.4) for the height zeta function ZU7,H(s) and that of the half-plane Hσ introduced before Theorem 2. Then recent work of la Bret`eche, Browning and Derenthal [10] has succeeded in establishing the following result. Theorem 4. There exists a constant α ∈ R, a”
• Singular del Pezzo surfaces whose universal torsors are hypersurfaces (2006, background): “It lead to the first complete proof of Manin’s conjecture for a singular cubic surface in [Der05] and [BBD05].”