From the viewpoint of mirror symmetry, we revisit the hypergeometric system $E(3, 6)$ for a family of K3 surfaces. We construct a good resolution of the Baily–Borel–Satake compactification of its parameter space, which admits special boundary points (LCSLs) given by normal crossing divisors. We find local isomorphisms between the $E(3, 6)$ systems and the associated GKZ systems defined locally on the parameter space and covering the entire parameter space. Parallel structures are conjectured in general for hypergeometric system $E(n, m)$ on Grassmannians. Local solutions and mirror symmetry will be described in a companion paper [20], where we introduce a K3 analogue of the elliptic lambda function in terms of genus two theta functions.

中文翻译：

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K3表面来自$ \ mathbb {P} ^ 2 $中的六行配置，镜像对称I

从镜像对称性的角度来看，我们重新审视了K3曲面族的超几何系统$ E（3，6）$。我们为其参数空间构造了一个Baily-Borel-Satake压缩的良好分辨率，它可以接受由法线交叉除数给出的特殊边界点（LCSL）。我们发现$ E（3，6）$系统与在参数空间上局部定义并覆盖整个参数空间的关联GKZ系统之间的局部同构。一般认为格拉斯曼方程的超几何系统$ E（n，m）$具有平行结构。局部解决方案和镜像对称性将在随附的论文[20]中进行介绍，在本文中，我们根据两个theta函数的种类介绍了椭圆lambda函数的K3类似物。