论文标题
在奇异性和模块化形式的kummer状表面上
On Kummer-like surfaces attached to singularity and modular forms
论文作者
论文摘要
我们研究一个晶格偏振$ k3 $的表面，这是源自主要极化的阿贝尔表面的kummer表面家族的延伸。我们的家人有两个特殊的特性。首先，它来自简单的$ k3 $奇异性的分辨率。其次，它具有四个复杂变量的遗传模块形式的自然参数化。在本文中，我们显示了两个结果：（1）我们确定了我们家庭的通用成员的先验晶格和Néron-Severi晶格。 （2）我们详细说明了与$ k3 $表面相关的双覆盖结构。
We study a family of lattice polarized $K3$ surfaces which is an extension of the family of Kummer surfaces derived from principally polarized Abelian surfaces. Our family has two special properties. First, it is coming from a resolution of a simple $K3$ singularity. Second, it has a natural parametrization by Hermitian modular forms of four complex variables. In this paper, we show two results: (1) We determine the transcendental lattice and the Néron-Severi lattice of a generic member of our family. (2) We give a detailed description of the double covering structure associated with our $K3$ surfaces.
