Cyclic Covers of the Projective Line
Cyclic Covers of the Projective Line
复制标题
投影线的循环覆盖
DOI：
10.1007/978-3-642-00639-5_3
复制
发表时间：
2009
期刊：
影响因子：
--
通讯作者：
J. Rohde
中科院分区：
文献类型：
--
作者：
J. Rohde
回想一下，我们将研究射影直线的循环覆盖族的霍奇结构的变化。此外，这类复盖的某些族适合于构造具有复乘法纤维稠密集的Calabi-Yau流形族。为了理解这类循环覆盖族的Hodge结构的变化，我们需要理解循环覆盖C → P1的Hodge结构。一个循环覆盖π：C → P1由下式给出，其中每个d是满足1 ≤dk≤ m −> 1的整数。数sdk不是由覆盖的同构类唯一确定的。然而，这些数字决定了覆盖的同构类，我们将在下面的章节中使用它们来计算Hodge结构的变化。
Recall that we will study variations of Hodge structures of families of cyclic coverings of the projective line. Moreover some families of such covers are suitable for the construction of families of Calabi-Yau manifolds with dense sets of complex multiplication fibers. In order to understand variations of Hodge structures of such families of cyclic coverings we need to understand the Hodge structure of a cyclic coveringC →P1.A cyclic coverπ:C →P1is given bywhere eachdkis an integer satisfying 1 ≤dk≤ m −> 1. The numbersdkare not uniquely determined by the isomorphism class of a cover. However, these numbers determine the isomorphism class of a cover and we will use them for the computation of the variation of Hodge structures in the following chapters.