| Introduction | p. 1 |
| An introduction to Hodge structures and Shimura varieties | p. 11 |
| The basic definitions | p. 12 |
| Jacobians, Polarizations and Riemann's Theorem | p. 19 |
| The definition of the Shimura datum | p. 25 |
| Hermitian symmetric domains | p. 35 |
| The construction of Shimura varieties | p. 43 |
| The definition of complex multiplication | p. 45 |
| Criteria and conjectures for complex multiplication | p. 50 |
| Cyclic covers of the projective line | p. 59 |
| Description of a cyclic cover of the projective line | p. 60 |
| The local system corresponding to a cyclic cover | p. 62 |
| The cohomology of a cover | p. 66 |
| Cyclic covers with complex multiplication | p. 67 |
| Some preliminaries for families of cyclic covers | p. 71 |
| The generic Hodge group | p. 71 |
| Families of covers of the projective line | p. 73 |
| The homology and the monodromy representation | p. 76 |
| The Galois group decomposition of the Hodge structure | p. 79 |
| The Galois group representation on the first cohomology | p. 79 |
| Quotients of covers and Hodge group decomposition | p. 84 |
| Upper bounds for the Mumford-Tate groups of the direct summands | p. 85 |
| A criterion for complex multiplication | p. 88 |
| The computation of the Hodge group | p. 91 |
| The monodromy group of an eigenspace | p. 92 |
| The Hodge group of a general direct summand | p. 99 |
| A criterion for the reaching of the upper bound | p. 102 |
| The exceptional cases | p. 106 |
| The Hodge group of a universal family of hyperelliptic curves | p. 110 |
| The complete generic Hodge group | p. 115 |
| Examples of families with dense sets of complex multiplication fibers | p. 121 |
| The necessary condition SINT | p. 121 |
| The application of SINT for the more complicated cases | p. 129 |
| The complete lists of examples | p. 136 |
| The derived variations of Hodge structures | p. 137 |
| The construction of Calabi-Yau manifolds with complex multiplication | p. 143 |
| The basic construction and complex multiplication | p. 143 |
| The Borcea-Voisin tower | p. 147 |
| The Viehweg-Zuo tower | p. 150 |
| A new example | p. 153 |
| The degree 3 case | p. 157 |
| Prelude | p. 158 |
| A modified version of the method of Viehweg and Zuo | p. 162 |
| The resulting family and its involutions | p. 166 |
| Other examples and variations | p. 169 |
| The degree 3 case | p. 170 |
| Calabi-Yau 3-manifolds obtained by quotients of degree 3 | p. 172 |
| The degree 4 case | p. 178 |
| Involutions on the quotients of the degree 4 example | p. 180 |
| The extended automorphism group of the degree 4 example | p. 183 |
| The automorphism group of the degree 5 example by Viehweg and Zuo | p. 185 |
| Examples of CMCY families of 3-manifolds and their invariants | p. 187 |
| The length of the Yukawa coupling | p. 187 |
| Examples obtained by degree 2 quotients | p. 188 |
| Examples obtained by degree 3 quotients | p. 189 |
| Outlook onto quotients by cyclic groups of high order | p. 196 |
| Maximal families of CMCY type | p. 199 |
| Facts about involutions and quotients of K3-surface | p. 199 |
| The associated Shimura datum | p. 201 |
| The examples | p. 203 |
| Examples of Calabi-Yau 3-manifolds with complex multiplication | p. 209 |
| Construction by degree 2 coverings of a ruled surface | p. 209 |
| Construction by degree 2 coverings of P2 | p. 214 |
| Construction by a degree 3 quotient | p. 217 |
| References | p. 223 |
| Index | p. 227 |
| Table of Contents provided by Ingram. All Rights Reserved. |
