**Fields Institute Monographs**

Volume: 22;
2005;
194 pp;
Hardcover

MSC: Primary 14; 11;

Print ISBN: 978-0-8218-3908-9

Product Code: FIM/22

List Price: $69.00

Individual Member Price: $55.20

**Electronic ISBN: 978-1-4704-3149-5
Product Code: FIM/22.E**

List Price: $69.00

Individual Member Price: $55.20

#### Supplemental Materials

# Modular Calabi-Yau Threefolds

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*Christian Meyer*

A co-publication of the AMS and Fields Institute

This book discusses the connection between Calabi-Yau
threefolds and modular forms. It presents the general theory and
brings together the known results. Hundreds of new examples are given
of rigid and non-rigid Calabi-Yau threefolds, and the construction of
correspondences between them leads to conjectures about the modular
forms involved. The author has compiled tables of newforms of weight
four and large levels, which are included in the appendix.

The great variety of new examples as well as the tables of newforms
makes this volume a valuable resource for graduate students and
researchers interested in algebraic geometry and arithmetic algebraic
geometry.

Titles in this series are co-published with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

#### Table of Contents

# Table of Contents

## Modular Calabi-Yau Threefolds

- Cover Cover11
- Title page iii4
- Contents v6
- Preface vii8
- Arithmetic on Calabi-Yau threefolds 112
- Fibre products of elliptic surfaces 2132
- Quintics in ℙ⁴ 3142
- Double octics 4758
- Other examples 107118
- Tables, correspondences, conclusions 135146
- Appendix A. Arrangements of eight planes 155166
- Appendix B. Modular double octics 163174
- Appendix C. Tables of weight two and weight four newforms 183194
- Bibliography 187198
- Index 193204
- Back Cover Back Cover1207

#### Readership

Graduate students and research mathematicians interested in algebraic geometry and arithmetic algebraic geometry.

#### Reviews

The present monograph is a nice addition to the existing literatures on arithmetic of Calabi-Yau varieties, and it will serve as a friendly introduction to graduate students as well as to researchers, who wish to learn about the arithmetic aspects of Calabi-Yau varieties.

-- Zentralblatt MATH