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.

引用

页码：1470 / 1479

页数：10

共 5 条

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Baragar, Arthur
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[3] Rational curves and points on K3 surfaces
Bogomolov, F
Tschinkel, Y
[J]. AMERICAN JOURNAL OF MATHEMATICS, 2005, 127 (04) : 825 - 835
[4] Fulton W., 1998, INTERSECTION THEORY, V2nd
[5] Hartshorne R., 1977, ALGEBRAIC GEOMETRY

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