Explicit Families of K3 Surfaces Having Real Multiplication

被引：0
|
作者：
Elsenhans, Andreas-Stephan [1 ]
Jahnel, Joerg [2 ]
机构：
[1] Univ Wurzburg, Inst Math, Emil-F-Str 30, D-97074 Wurzburg, Germany
[2] Univ Siegen, Dept Math, Walter-Flex-Str 3, D-57068 Siegen, Germany
来源：
MICHIGAN MATHEMATICAL JOURNAL | 2023年 / 73卷 / 01期
关键词：
CONJECTURE;
D O I：
10.1307/mmj/20205878
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For families of K3 surfaces, we establish a sufficient cri-terion for real or complex multiplication. Our criterion is arithmetic in nature. It may show, at first, that the generic fibre of the family has a nontrivial endomorphism field. Moreover, the endomorphism field does not shrink under specialization. As an application, we present two explicit families of K3 surfaces having real multiplication by ./ ./ Q( 2) and Q( 5), respectively.
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页码：3 / 32
页数：30
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