Rational points on the E6 cubic surface.

机译：E6立方曲面上的有理点。

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Manin and others have formulated a program for counting rational points of bounded height on Fano varieties over number fields. Recent attention has been given to the role universal torsors play in this problem. We prove Peyre's refined version of Manin's conjecture for the unique split singular cubic surface with a singularity of type E6 defined over Q . The proof makes uses of the universal torsor of the surface and is an adaptation of the method used by Salberger to prove Manin's conjecture for split toric varieties over Q .

机译：Manin和其他人制定了一个程序，用于计算数字字段上Fano品种的有界高度的有理点。最近，人们已经关注了通用转矩在此问题中的作用。我们证明了Peyre对Manin猜想的改进版本，该奇异猜想是唯一的分裂奇异三次曲面，其奇异性在Q上定义为E6类型。该证明利用了表面的通用扭转，并且是Salberger用于证明Manin对Q上复曲面复曲面变种的猜想的一种方法的改编。

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作者
Joyce, Michael.;
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作者单位

Brown University.;

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授予单位 Brown University.;
学科 Mathematics.
学位 Ph.D.
年度 2005
页码 45 p.
总页数 45
原文格式 PDF
正文语种 eng
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Rational points on the E6 cubic surface.

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