关于与奇点和模形式相关的类Kummer曲面
On Kummer-like surfaces attached to singularity and modular forms
AI总结：
本研究扩展了源自主极化阿贝尔曲面的Kummer曲面族，提出一类由简单$K3$奇点消解得到、可通过四复变量Hermitian模形式参数化的格极化$K3$曲面，确定了其一般成员的超越格与Néron-Severi格，并详细描述了相关双复盖结构。
摘要：
我们研究一类格极化的$K3$曲面，它是源自主极化阿贝尔曲面的Kummer曲面族的扩展。我们的曲面族有两个特殊性质：第一，它源于一个简单$K3$奇点的消解；第二，它可通过四个复变量的Hermitian模形式进行自然参数化。本文中我们给出两个结果：（1）确定了该曲面族一般成员的超越格和Néron-Severi格；（2）对与我们的$K3$曲面相关的双复盖结构进行了详细描述。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
