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# Counting Rational Points on Ruled Varieties

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Published:2004-06-01
Printed: Jun 2004
• David McKinnon
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## Abstract

In this paper, we prove a general result computing the number of rational points of bounded height on a projective variety $V$ which is covered by lines. The main technical result used to achieve this is an upper bound on the number of rational points of bounded height on a line. This upper bound is such that it can be easily controlled as the line varies, and hence is used to sum the counting functions of the lines which cover the original variety $V$.
 MSC Classifications: 11G50 - Heights [See also 14G40, 37P30] 11D45 - Counting solutions of Diophantine equations 11D04 - Linear equations 14G05 - Rational points

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