Cyclic coverings, Calabi-Yau manifolds and complex multiplication /

Cyclic coverings, Calabi-Yau manifolds and complex multiplication /

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Bibliographic Details
Author / Creator:	Rohde, Jan Christian.
Imprint:	Dordrecht ; London : Springer, 2009.
Description:	1 online resource (ix, 228 pages) : illustrations.
Language:	English
Series:	Lecture notes in mathematics, 1617-9692 ; 1975 Lecture notes in mathematics (Springer-Verlag) ; 1975.
Subject:	Calabi-Yau manifolds. Multiplication, Complex. Calabi-Yau manifolds. Multiplication, Complex.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11072854

Hidden Bibliographic Details
ISBN:	9783642006395 3642006396 9783642006388
Notes:	Title from PDF title page (SpringerLink, viewed Dec. 6, 2009). Revision of work originally presented as the author's doctoral thesis-- Universität Duisburg-Essen, 2007. Includes bibliographical references and index.
Summary:	The main goal of this book is the construction of families of Calabi-Yau 3-manifolds with dense sets of complex multiplication fibers. The new families are determined by combining and generalizing two methods. Firstly, the method of E. Viehweg and K. Zuo, who have constructed a deformation of the Fermat quintic with a dense set of CM fibers by a tower of cyclic coverings. Using this method, new families of K3 surfaces with dense sets of CM fibers and involutions are obtained. Secondly, the construction method of the Borcea-Voisin mirror family, which in the case of the author's examples yields families of Calabi-Yau 3-manifolds with dense sets of CM fibers, is also utilized. Moreover fibers with complex multiplication of these new families are also determined. This book was written for young mathematicians, physicists and also for experts who are interested in complex multiplication and varieties with complex multiplication. The reader is introduced to generic Mumford-Tate groups and Shimura data, which are among the main tools used here. The generic Mumford-Tate groups of families of cyclic covers of the projective line are computed for a broad range of examples.
Other form:	Print version: Rohde, Jan Christian. Cyclic coverings, Calabi-Yau manifolds and complex multiplication. Dordrecht ; London : Springer, 2009 9783642006388

Description
Summary:	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.
Item Description:	Title from PDF title page (SpringerLink, viewed Dec. 6, 2009). Revision of work originally presented as the author's doctoral thesis-- Universität Duisburg-Essen, 2007.
Physical Description:	1 online resource (ix, 228 pages) : illustrations.
Bibliography:	Includes bibliographical references and index.
ISBN:	9783642006395 3642006396 9783642006388
ISSN:	1617-9692 ;