规则簇上有理点的计数
Counting Rational Points on Ruled Varieties
摘要：
本文证明了一个计算被直线覆盖的射影簇$V$上有界高的有理点个数的一般结果。用于实现这一点的主要技术结果是一个上限的有理点的数量有界的高度线。该上界是这样的，即当线变化时，它可以容易地控制，并因此用于对覆盖原始品种$V$的线的计数函数求和。
英文摘要：
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 $V$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
