By Christian Rohde

ISBN-10: 3642006388

ISBN-13: 9783642006388

Calabi-Yau manifolds were an item of in depth learn over the past 20 years. one of many purposes is the significance of Calabi-Yau 3-manifolds in sleek physics - particularly string conception. an enticing category of Calabi-Yau manifolds is given by way of 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 target of this e-book to build households of Calabi-Yau 3-manifolds with dense units of ?bers with advanced multiplication. so much - amples during this publication are developed utilizing households of curves with dense units of ?bers with CM. The contents of this booklet can approximately be divided into elements. The ?rst six chapters care for households of curves with dense units of CM ?bers and introduce the mandatory theoretical historical past. This comprises between different issues a number of facets of Hodge conception and Shimura forms. utilizing the ?rst half, households of Calabi-Yau 3-manifolds with dense units of ?bers withCM are built within the final ?ve chapters. within the appendix one ?nds examples of Calabi-Yau 3-manifolds with advanced mul- plication which aren't unavoidably ?bers of a kin with a dense set ofCM ?bers. the writer hopes to have succeeded in writing a readable publication which may even be utilized by non-specialists.

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Cyclic Coverings, Calabi-Yau Manifolds and Complex Multiplication (Lecture Notes in Mathematics) by Christian Rohde

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