Cyclic Coverings, Calabi-Yau Manifolds and Complex Multiplication (Paperback, 2009 ed.)

Calabi-Yau manifolds have been an object of extensive research during the last two decades. One of the reasons is the importance of Calabi-Yau 3-manifolds in modern physics - notably string theory. An interesting class of Calabi-Yau manifolds is given by those with complex multiplication (CM). Calabi-Yau manifolds with CM are also of interest in theoretical physics, e. g. in connection with mirror symmetry and black hole attractors. It is the main aim of this book to construct families of Calabi-Yau 3-manifolds with dense sets of ?bers with complex multiplication. Most - amples in this book are constructed using families of curves with dense sets of ?bers with CM. The contents of this book can roughly be divided into two parts. The ?rst six chapters deal with families of curves with dense sets of CM ?bers and introduce the necessary theoretical background. This includes among other things several aspects of Hodge theory and Shimura varieties. Using the ?rst part, families of Calabi-Yau 3-manifolds with dense sets of ?bers withCM are constructed in the remaining ?ve chapters. In the appendix one ?nds examples of Calabi-Yau 3-manifolds with complex mul- plication which are not necessarily ?bers of a family with a dense set ofCM ?bers. The author hopes to have succeeded in writing a readable book that can also be used by non-specialists.

General

Imprint:	Springer-Verlag
Country of origin:	Germany
Series:	Lecture Notes in Mathematics, 1975
Release date:	April 2009
First published:	2009
Authors:	Christian Rohde
Dimensions:	235 x 155 x 13mm (L x W x T)
Format:	Paperback
Pages:	228
Edition:	2009 ed.
ISBN-13:	978-3-642-00638-8
Categories:	Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry
LSN:	3-642-00638-8
Barcode:	9783642006388

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