RATIONAL CURVES ON ELLIPTIC SURFACES

被引：5

作者：

Ulmer, Douglas ^{[1
]}

机构：

[1] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

来源：

JOURNAL OF ALGEBRAIC GEOMETRY | 2017年 / 26卷 / 02期

关键词：

VARIETIES; SECTION; FIELDS; RANK;

D O I：

10.1090/jag/680

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that a very general elliptic surface epsilon -> P-1 over the complex numbers with a section and with geometric genus pg >= 2 contains no rational curves other than the section and components of singular fibers. Equivalently, if E/C(t) is a very general elliptic curve of height d >= 3 and if L is a finite extension of C(t) with L congruent to C(u), then the Mordell-Weil group E(L) = 0.

引用

页码：357 / 377

页数：21

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