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Cyclic Coverings, Calabi-Yau Manifolds and Complex Multiplication (Lecture Notes in Mathematics, 1975) - Softcover
Synopsis
This book constructs families of Calabi-Yau 3-manifolds with dense sets of complex multiplication fibers, which are determined by combining the method of E. Viehweg and K. Zuo with the construction method of the Borcea-Voisin mirror family.
"synopsis" may belong to another edition of this title.
From the Back Cover
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.
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- PublisherSpringer
- Publication date2009
- ISBN 10 3642006388
- ISBN 13 9783642006388
- BindingPaperback
- LanguageEnglish
- Number of pages237
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Cyclic Coverings, Calabi-Yau Manifolds and Complex Multiplication (Lecture Notes in Mathematics, 1975)
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Cyclic Coverings, Calabi-Yau Manifolds and Complex Multiplication
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Cyclic Coverings, Calabi-Yau Manifolds and Complex Multiplication (Lecture Notes in Mathematics, 1975)
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Cyclic Coverings, Calabi-Yau Manifolds and Complex Multiplication
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Springer Berlin Heidelberg Apr 2009, 2009
ISBN 10: 3642006388
ISBN 13: 9783642006388
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 244 pp. Englisch. Seller Inventory # 9783642006388
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Cyclic Coverings, Calabi-Yau Manifolds and Complex Multiplication
Published by
Springer Berlin Heidelberg, 2009
ISBN 10: 3642006388
ISBN 13: 9783642006388
New
Taschenbuch
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Seller Inventory # 9783642006388
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Cyclic Coverings, Calabi-yau Manifolds and Complex Multiplication
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Cyclic Coverings, Calabi-Yau Manifolds and Complex Multiplication
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Springer Berlin Heidelberg, 2009
ISBN 10: 3642006388
ISBN 13: 9783642006388
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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 th. Seller Inventory # 5043167
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