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).

Readership

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

Table of Contents

• Arithmetic on Calabi-Yau threefolds
• Fibre products of elliptic surfaces
• Quintics in $\mathbb{P}^4$
• Double octics
• Other examples
• Tables, correspondences, conclusions
• Arrangements of eight planes
• Modular double octics
• Tables of weight two and weight four newforms
• Bibliography
• Index