Counting Rational Points on Ruled Varieties

Details Counting Rational Points on Ruled Varieties Counting Rational Points on Ruled Varieties

2002-07-10

arxiv.org/abs/math/0207088v1

Mathematics

Algebraic Geometry

LaTeX, 9 pages, no figures

Scientific paper

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 $V$.

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