Modular Calabi-Yau Threefolds (Fields Institute Monographs)

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. "The main subject of this book is the connection between Calabi-Yau threefolds and modular forms. The book presents the general theory and brings together the known results. It studies hundreds of new examples of rigid and non-rigid modular Calabi-Yau threefolds and correspondences between them. Conjectures about the possible levels of modular forms connected with Calabi-Yau threefolds are presented. Tables of newforms of weight four and large levels are compiled and included in the appendix."--Jacket

The main subject of this book is the connection between Calabi-Yau threefolds and modular forms. The book presents the general theory and brings together the known results. It studies hundreds of new examples of rigid and non-rigid modular Calabi-Yau threefolds and correspondences between them. Conjectures about the possible levels of modular forms connected with Calabi-Yau threefolds are presented. Tables of newforms of weight four and large levels are compiled and included in the appendix.

Cover Title page Contents Preface Arithmetic on Calabi-Yau threefolds Fibre products of elliptic surfaces Quintics in P4 Double octics Other examples Tables, correspondences, conclusions Appendix A. Arrangements of eight planes Appendix B. Modular double octics Appendix C. Tables of weight two and weight four newforms Bibliography Index Back Cover Discusses the connection between Calabi-Yau threefolds and modular forms. This title presents the general theory and brings together the known results. It features hundreds of examples of rigid and non-rigid Calabi-Yau threefolds, and the construction of correspondences between them leads to conjectures about the modular forms involved.