Theta functions on the bounded symmetric domain of typeI2, 2 and the period map of a 4-parameter family of K3 surfaces
Theta functions on the bounded symmetric domain of typeI2, 2 and the period map of a 4-parameter family of K3 surfaces
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Theta 函数作用于 I2、2 型有界对称域和 K3 表面 4 参数族的周期图
DOI：
10.1007/bf01444893
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发表时间：
1993
影响因子：
1.4
通讯作者：
Keiji Matsumoto
中科院分区：
文献类型：
--
作者：
Keiji Matsumoto
本文是[MSY 2]的继续，其中研究了四维K3-曲面族的周期映射，即沿沿着六条线的~ 2分支的双覆盖.本文用θ函数给出了12，2型对称域上周期映射的逆。经典的椭圆曲线族的周期映射是It '1在四点分支的双覆盖，它通过水平2的主同余子群F（2）将lP 1上四点的交换空间X（2，4）送到上半空间lH的商空间. X（2，4）的任何元素由2 × 4 C矩阵x=（Xsk）表示，其列是点的齐次坐标;空间X（2，4）可以通过以下映射在] p2中实现：1：X~[D12（x）D34（X），D13（X）D24（x），D14（x）Dz 3（x）]，其中Djk（x）= det（xls Xlk '~。x2j X2k/
This paper is a continuation of [MSY2], in which the period map of the 4-dimensional family of K3-surfaces, the double covers of~ 2 branching along six lines, is studied. In this paper the inverse of the period map is given by theta functions on the symmetric domain of type 12, 2. Classically the period map of the family of elliptic curves, which are the double covers of It'1 branching at four points, sends the configulation space X (2, 4) of four points on lP 1 to the quotient space of the upper half space lH by the principal congruence subgroup F (2) of level 2. Any element of X (2, 4) is represented by a 2 x 4 C-matrix x=(Xsk), whose columns are homogeneous coordinates of the points; the space X (2, 4) can be realized in] p2 by the following map: l: X~[D12 (x) D34 (X), DI3 (X) D24 (x), D14 (x) Dz3 (x)], whereDjk (x)= det (xls Xlk'~.\x2j X2k/
影响因子：
1.7
作者：
J. Igusa
通讯作者：
J. Igusa