Download PDF by Christian Rohde: Cyclic Coverings, Calabi-Yau Manifolds and Complex

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 - particularly string concept. a fascinating classification of Calabi-Yau manifolds is given via people with advanced 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 objective of this publication to build households of Calabi-Yau 3-manifolds with dense units of ?bers with advanced multiplication. so much - amples during this e-book are developed 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 care for households of curves with dense units of CM ?bers and introduce the mandatory theoretical history. This comprises between different issues a number of features of Hodge thought and Shimura types. 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 unavoidably ?bers of a kinfolk with a dense set ofCM ?bers. the writer hopes to have succeeded in writing a readable booklet that may even be utilized by non-specialists.