Fields Institute Monographs 2005; 194 pp; hardcover Volume: 22 ISBN10: 082183908X ISBN13: 9780821839089 List Price: US$69 Member Price: US$55.20 Order Code: FIM/22
 This book discusses the connection between CalabiYau threefolds and modular forms. It presents the general theory and brings together the known results. Hundreds of new examples are given of rigid and nonrigid CalabiYau 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 copublished 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. Reviews "The present monograph is a nice addition to the existing literatures on arithmetic of CalabiYau 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 CalabiYau varieties."  Zentralblatt MATH Table of Contents  Arithmetic on CalabiYau 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
