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

页码：89 / 114

页数：26

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