The normalizer of the level (2,2)-Heisenberg Group
The normalizer of the level (2,2)-Heisenberg Group
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(2,2) 级的归一化器-海森堡群
DOI：
10.1007/bf02567760
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发表时间：
1992
影响因子：
0.6
通讯作者：
I. Nieto
中科院分区：
文献类型：
--
作者：
I. Nieto
摘要Mumford在[Mu]中首次引入的水平(2,2)-Heisenberg群pg（2,2）是一个32阶的子群inSL（4,）。设n为g (2,2) inSL（4,）的归一化式。本文明确地描述了n /G（2,2）到对称群的两个自然同构
$$\mathbb{S}_6 $$
6个元素。这些识别澄清了经典论文中的计算，例如[Hu]中的Kummer曲面理论和[Je]中的二次线复合体理论，并将在[Nie]中用于描述具有水平（2,6）结构的阿贝尔曲面的模空间。
AbstractThe level (2, 2)-Heisenberg GroupG(2, 2) as first introduced by Mumford in [Mu] is a subgroup inSL(4,ℂ) of order 32. LetN be the normalizer ofG(2, 2) inSL(4,ℂ).This note describes explicitely the two natural isomorphisms fromN/G(2, 2) to the symmetric group
$$\mathbb{S}_6 $$
of 6 elements. These identifications clarify the computations in the classical treatises as for example in the theory of Kummer surfaces in [Hu] and the theory of the quadric line complex as in [Je] and will be used in [Nie] to describe the moduli space for abelian surfaces with a level (2, 6)-structure.