论文标题
在皮卡德等级的K3表面14
On K3 surfaces of Picard rank 14
论文作者
论文摘要
我们研究了具有有限的自动形态基团的复杂代数K3表面，并通过排名四元素的晶格两极化。存在三个这样的晶格，即$ h \ oplus e_8（-1）\ oplus a_1（-1）^{\ oplus 4} $，$ h \ oplus e_8（-1）\ oplus d_4（-1）$作为我们研究的一部分，我们为这些表面提供了异常模型，作为四分之一的投影性超曲面，并用合适的模块化不变剂来描述相关的粗模量空间。此外，我们探讨了这些家庭与通过Nikulin Construction相关的双重K3家庭之间的联系。
We study complex algebraic K3 surfaces with finite automorphism groups and polarized by rank-fourteen, 2-elementary lattices. Three such lattices exist, namely $H \oplus E_8(-1) \oplus A_1(-1)^{\oplus 4}$, $H \oplus E_8(-1) \oplus D_4(-1)$, and $H \oplus D_8(-1) \oplus D_4(-1)$. As part of our study, we provide birational models for these surfaces as quartic projective hypersurfaces and describe the associated coarse moduli spaces in terms of suitable modular invariants. Additionally, we explore the connection between these families and dual K3 families related via the Nikulin construction.
