Cyclic Coverings, Calabi-Yau Manifolds and Complex Multiplication
Cyclic Coverings, Calabi-Yau Manifolds and Complex Multiplication
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DOI：
10.1007/978-3-642-00639-5
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发表时间：
2007-11
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影响因子：
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通讯作者：
J. Rohde
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文献类型：
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作者：
J. Rohde
在过去的二十年里，卡-丘流形一直是广泛研究的对象。原因之一是卡-丘三维流形在现代物理学中的重要性，特别是弦理论。一类有趣的Calabi-Yau流形是由具有复数乘法（CM）的流形给出的。具有CM的卡-丘流形在理论物理学中也很有趣，例如与镜像对称和黑洞吸引子有关。这是这本书的主要目的是建立家庭的卡-丘3-流形与稠密集？与复数乘法。大多数样本在这本书中使用的曲线与密集集？与CM。这本书的内容大致可以分为两部分。什么？前六章处理家庭的曲线与密集集的CM？并介绍了必要的理论背景。这包括霍奇理论和志村变种的几个方面。利用？第一部分，具有稠密集的Calabi-Yau 3-流形族。与CM的ber是在其余的？五章。在附录一？给出了具有复数乘法的Calabi-Yau 3-流形的例子，这些例子不一定是？一个拥有密集CM集的家庭的成员？贝尔。作者希望能成功地写出一本可读的书，也能被非专业人士使用。
Calabi-Yau manifolds have been an object of extensive research during the last two decades. One of the reasons is the importance of Calabi-Yau 3-manifolds in modern physics-notably string theory. An interesting class of Calabi-Yau manifolds is given by those with complex multiplication (CM). Calabi-Yau manifolds with CM are also of interest in theoretical physics, eg in connection with mirror symmetry and black hole attractors. It is the main aim of this book to construct families of Calabi-Yau 3-manifolds with dense sets of? bers with complex multiplication. Most-amples in this book are constructed using families of curves with dense sets of? bers with CM. The contents of this book can roughly be divided into two parts. The? rst six chapters deal with families of curves with dense sets of CM? bers and introduce the necessary theoretical background. This includes among other things several aspects of Hodge theory and Shimura varieties. Using the? rst part, families of Calabi-Yau 3-manifolds with dense sets of? bers withCM are constructed in the remaining? ve chapters. In the appendix one? nds examples of Calabi-Yau 3-manifolds with complex mul-plication which are not necessarily? bers of a family with a dense set ofCM? bers. The author hopes to have succeeded in writing a readable book that can also be used by non-specialists.