Manin’s conjecture for a certain singular cubic surface
نویسنده
چکیده
This paper contains a proof of Manin’s conjecture for the singular cubic surface S ⊂ P with a singularity of type E6, defined by the equation x1x 2 2 + x2x 2 0 + x 3 3 = 0. If U is the open subset of S obtained by deleting the unique line from S, then the number of rational points in U with anticanonical height bounded by B behaves asymptotically as cB(logB), where the constant c agrees with the one conjectured by Peyre.
منابع مشابه
The density of rational points on a certain singular cubic surface
We show that the number of non-trivial rational points of height at most B, which lie on the cubic surface x1x2x3 = x4(x1 + x2 + x3) , has order of magnitude B(log B). This agrees with Manin’s conjecture.
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