Calabi-Yau manifolds were an item of intensive examine over the past 20 years. one of many purposes is the significance of Calabi-Yau 3-manifolds in smooth physics - significantly string conception. an enticing type of Calabi-Yau manifolds is given by way of people with advanced multiplication (CM). Calabi-Yau manifolds with CM also are of curiosity in theoretical physics, e. g. in reference to replicate symmetry and black gap attractors. it's the major goal of this booklet to build households of Calabi-Yau 3-manifolds with dense units of ?bers with advanced multiplication. so much - amples during this ebook are built utilizing households of curves with dense units of ?bers with CM. The contents of this e-book can approximately be divided into components. The ?rst six chapters take care of households of curves with dense units of CM ?bers and introduce the required theoretical historical past. This contains between different issues a number of points of Hodge idea and Shimura kinds. utilizing the ?rst half, households of Calabi-Yau 3-manifolds with dense units of ?bers withCM are developed within the last ?ve chapters. within the appendix one ?nds examples of Calabi-Yau 3-manifolds with complicated mul- plication which aren't unavoidably ?bers of a kinfolk with a dense set ofCM ?bers. the writer hopes to have succeeded in writing a readable booklet that could even be utilized by non-specialists.
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