K3 surfaces, rational curves, and rational points

被引：5
|
作者：
Baragar, Arthur [2 ]
McKinnon, David [1 ]
机构：
[1] Univ Waterloo, Dept Pure Math, Waterloo, ON N2L 3G1, Canada
[2] Univ Nevada, Dept Math Sci, Las Vegas, NV 89154 USA
来源：
JOURNAL OF NUMBER THEORY | 2010年 / 130卷 / 07期
基金：
加拿大自然科学与工程研究理事会;
关键词：
K3; surface; Rational curve; Rational point; Bogomolov; Elliptic surface;
D O I：
10.1016/j.jnt.2010.02.014
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove that for any of a wide class of elliptic surfaces X defined over a number field k, if there is an algebraic point on X that lies on only finitely many rational curves, then there is an algebraic point on x that lies on no rational curves. In particular, our theorem applies to a large class of elliptic K3 surfaces, which relates to a question posed by Bogomolov in 1981. (C) 2010 Elsevier Inc. All rights reserved.
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页码：1470 / 1479
页数：10
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