Calabi-Yau manifolds were an item of in depth examine over the last twenty years. one of many purposes is the significance of Calabi-Yau 3-manifolds in glossy physics - particularly string thought. an engaging category of Calabi-Yau manifolds is given via people with complicated 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 publication to build households of Calabi-Yau 3-manifolds with dense units of ?bers with complicated multiplication. such a lot - amples during this booklet are developed utilizing households of curves with dense units of ?bers with CM. The contents of this publication 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 numerous elements of Hodge concept and Shimura types. utilizing the ?rst half, households of Calabi-Yau 3-manifolds with dense units of ?bers withCM are built within the ultimate ?ve chapters. within the appendix one ?nds examples of Calabi-Yau 3-manifolds with complicated mul- plication which aren't inevitably ?bers of a kin with a dense set ofCM ?bers. the writer hopes to have succeeded in writing a readable ebook that may even be utilized by non-specialists.

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