Skip to main content
SpringerLink
Log in
Book cover

Cyclic Coverings, Calabi-Yau Manifolds and Complex Multiplication

  • Book
  • © 2009

Overview

Authors:
  1. Christian Rohde
    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Lecture Notes in Mathematics (LNM, volume 1975)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (12 chapters)

  1. Front Matter

    Pages 1-7
    Download chapter PDF

  2. Introduction

    • Jan Christian Rohde
    Pages 1-9

  3. An Introduction to Hodge Structures and Shimura Varieties

    • Jan Christian Rohde
    Pages 11-57

  4. Cyclic Covers of the Projective Line

    • Jan Christian Rohde
    Pages 59-69

  5. Some Preliminaries for Families of Cyclic Covers

    • Jan Christian Rohde
    Pages 71-78

  6. The Galois Group Decomposition of the Hodge Structure

    • Jan Christian Rohde
    Pages 79-89

  7. The Computation of the Hodge Group

    • Jan Christian Rohde
    Pages 91-119

  8. Examples of Families with Dense Sets of Complex Multiplication Fibers

    • Jan Christian Rohde
    Pages 121-142

  9. The Construction of Calabi-Yau Manifolds with Complex Multiplication

    • Jan Christian Rohde
    Pages 143-156

  10. The Degree 3 Case

    • Jan Christian Rohde
    Pages 157-167

  11. Other Examples and Variations

    • Jan Christian Rohde
    Pages 169-186

  12. Examples of CMCY Families of 3-manifolds and their Invariants

    • Jan Christian Rohde
    Pages 187-198

  13. Maximal Families of CMCY Type

    • Jan Christian Rohde
    Pages 199-208

  14. Back Matter

    Pages 1-24
    Download chapter PDF
Back to top

Keywords

About this book

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.

Bibliographic Information

  • Book Title: Cyclic Coverings, Calabi-Yau Manifolds and Complex Multiplication

  • Authors: Christian Rohde

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-642-00639-5

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2009

  • Softcover ISBN: 978-3-642-00638-8Published: 28 April 2009

  • eBook ISBN: 978-3-642-00639-5Published: 12 June 2009

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: IX, 228

  • Topics: Algebraic Geometry

Publish with us

Policies and ethics

Back to top

Search

Navigation