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Counting Rational Points on Ruled Varieties

Published online by Cambridge University Press:  20 November 2018

David McKinnon
David McKinnon*
Affiliation:
Department of Pure Mathematics University of Waterloo Waterloo, Ontario N2L 3G1, email: dmckinnon@math.uwaterloo.ca
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Abstract

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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 $V$.

Keywords

11G5011D4511D0414G05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 47 , Issue 2 , 01 June 2004 , pp. 264 - 270
Copyright
Copyright © Canadian Mathematical Society 2004

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