Cyclic Coverings, Calabi-Yau Manifolds and Complex Multiplication
The main goal of this book is the construction of families of Calabi-Yau 3-manifolds with dense sets of complex multiplication fibers. The new families are determined by combining and generalizing two methods. Firstly, the method of E. Viehweg and K. Zuo, who have constructed a deformation of the Fe...
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| Format: | Electronic |
| Language: | English |
| Published: |
Berlin, Heidelberg :
Springer Berlin Heidelberg,
2009.
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| Series: | Lecture Notes in Mathematics,
1975 |
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| Online Access: | https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-642-00639-5 |
Table of Contents:
- 1 An introduction to Hodge structures and Shimura varieties
- 2 Cyclic covers of the projective line
- 3 Some preliminaries for families of cyclic covers
- 4 The Galois group decomposition of the Hodge structure
- 5 The computation of the Hodge group
- 6 Examples of families with dense sets of complex multiplication fibers
- 7 The construction of Calabi-Yau manifolds with complex multiplication
- 8 The degree 3 case
- 9 Other examples and variations
- 10 Examples of CMCY families of 3-manifolds and their invariants
- 11 Maximal families of CMCY type.