K3 surfaces from configurations of six lines in P2 and mirror symmetry II-- λK3 -functions
K3 surfaces from configurations of six lines in P2 and mirror symmetry II-- λK3 -functions
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K3 表面来自 P2 中的六条线的配置和镜像对称 II-- λK3 - 函数
DOI：
10.1093/imrn/rnz259
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发表时间：
2019
影响因子：
1
通讯作者：
B.H. Lian and S.-T. Yau
中科院分区：
文献类型：
--
作者：
S. Hosono;B.H. Lian and S.-T. Yau
我们继续研究了描述双覆盖族K3曲面周期积分的超几何系统。在K3曲面模空间中的某些特殊边界点附近，我们构造了局部解，并确定了用亏格2 θ函数表示的镜像映射.这些镜像映射是椭圆函数的K3类似物。我们发现在模空间中对应于翻转的lambda函数有两个非同构的定义。我们还讨论了双覆盖K3曲面的镜像对称性及其高维推广。一份后续文件将更详细地介绍后者。
We continue our study on the hypergeometric systemthat describes period integrals of the double cover family of K3 surfaces. Near certain special boundary points in the moduli space of the K3 surfaces, we construct the local solutions and determine the so-called mirror maps expressing them in terms of genus 2 theta functions. These mirror maps are the K3 analogues of the elliptic-function. We find that there are two nonisomorphic definitions of the lambda functions corresponding to a flip in the moduli space. We also discuss mirror symmetry for the double cover K3 surfaces and their higher dimensional generalizations. A follow-up paper will describe more details of the latter.