Read e-book online Cyclic Coverings, Calabi-Yau Manifolds and Complex PDF

By Christian Rohde

Calabi-Yau manifolds were an item of intensive learn over the past twenty years. one of many purposes is the significance of Calabi-Yau 3-manifolds in glossy physics - significantly 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 reflect symmetry and black gap attractors. it's the major goal of this ebook to build households of Calabi-Yau 3-manifolds with dense units of ?bers with complicated multiplication. such a lot - amples during this ebook are developed utilizing households of curves with dense units of ?bers with CM. The contents of this ebook can approximately be divided into components. The ?rst six chapters care for households of curves with dense units of CM ?bers and introduce the mandatory theoretical history. This comprises between different issues numerous features of Hodge concept and Shimura kinds. utilizing the ?rst half, households of Calabi-Yau 3-manifolds with dense units of ?bers withCM are developed within the closing ?ve chapters. within the appendix one ?nds examples of Calabi-Yau 3-manifolds with advanced 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 publication which could even be utilized by non-specialists.

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