Modular map for the family of abelian surfaces via elliptic K3 surfaces

被引：6
作者：
Nagano, Atsuhira [1 ]
Shiga, Hironori [2 ]
机构：
[1] Waseda Univ, Dept Math, Shinjuku Ku, Tokyo 1698555, Japan
[2] Chiba Univ, Grad Sch Sci, Inage Ku, Chiba 2638522, Japan
来源：
MATHEMATISCHE NACHRICHTEN | 2015年 / 288卷 / 01期
基金：
日本学术振兴会;
关键词：
Abelian surfaces; K3; surfaces; Hilbert modular forms; period domains; theta constants; FORMS; EQUATIONS;
D O I：
10.1002/mana.201300142
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we give explicit modular maps for the family of abelian surfaces and that of the abelian surfaces whose endomorphism algebra contains Zinverted right perpendicular (1 + root 5)/2inverted left perpendicular. We obtain a description of the Shimura variety for the latter family, also. The notion of the family of K3 surfaces with a fixed marking plays a central role. As the basement of our study we use the expressions of those families given by Clingher-Doran, A. Nagano and the work of A. Kumar as well. (C) 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
引用
收藏
页码：89 / 114
页数：26
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