Cyclic Coverings, Calabi-Yau Manifolds and Complex Multiplication (Record no. 31209)
[ view plain ]
| 000 -LEADER | |
|---|---|
| fixed length control field | 03135nam a22004095i 4500 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9783642006395 |
| -- | 978-3-642-00639-5 |
| 100 1# - MAIN ENTRY--AUTHOR NAME | |
| Personal name | Rohde, Christian. |
| 245 10 - TITLE STATEMENT | |
| Title | Cyclic Coverings, Calabi-Yau Manifolds and Complex Multiplication |
| Statement of responsibility, etc | by Christian Rohde. |
| 260 #1 - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication | Berlin, Heidelberg : |
| Name of publisher | Springer Berlin Heidelberg, |
| Year of publication | 2009. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Other physical details | online resource. |
| 490 1# - SERIES STATEMENT | |
| Series statement | Lecture Notes in Mathematics, |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | An Introduction to Hodge Structures and Shimura Varieties -- Cyclic Covers of the Projective Line -- Some Preliminaries for Families of Cyclic Covers -- The Galois Group Decomposition of the Hodge Structure -- The Computation of the Hodge Group -- Examples of Families with Dense Sets of Complex Multiplication Fibers -- The Construction of Calabi-Yau Manifolds with Complex Multiplication -- The Degree 3 Case -- Other Examples and Variations -- Examples of Families of 3-manifolds and their Invariants -- Maximal Families of CMCY Type. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | 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. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Mathematics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Geometry, algebraic. |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Mathematics. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Algebraic Geometry. |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | http://dx.doi.org/10.1007/978-3-642-00639-5 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | E-BOOKS |
| 264 #1 - | |
| -- | Berlin, Heidelberg : |
| -- | Springer Berlin Heidelberg, |
| -- | 2009. |
| 336 ## - | |
| -- | text |
| -- | txt |
| -- | rdacontent |
| 337 ## - | |
| -- | computer |
| -- | c |
| -- | rdamedia |
| 338 ## - | |
| -- | online resource |
| -- | cr |
| -- | rdacarrier |
| 347 ## - | |
| -- | text file |
| -- | |
| -- | rda |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| -- | 0075-8434 ; |
| Withdrawn status | Lost status | Damaged status | Not for loan | Current library | Accession Number | Uniform Resource Identifier | Koha item type |
|---|---|---|---|---|---|---|---|
| IMSc Library | EBK1915 | http://dx.doi.org/10.1007/978-3-642-00639-5 | E-BOOKS |