Arithmetic of Complex Manifolds Proceedings of a Conference held in Erlangen, FRG, May 27-31, 1988

It was the aim of the Erlangen meeting in May 1988 to bring together number theoretists and algebraic geometers to discuss problems of common interest, such as moduli problems, complex tori, integral points, rationality questions, automorphic forms. In recent years such problems, which are simultaneously of arithmetic and geometric interest, have become increasingly important. This proceedings volume contains 12 original research papers. Its main topics are theta functions, modular forms, abelian varieties and algebraic three-folds.

Surfaces on quintic threefolds associated to the Horrocks-Mumford bundle.- Curves of genus three on a general abelian threefold and the non-finite generation of the Griffiths group.- Sur les fonctions theta du second ordre.- Une demonstration elementaire du theoreme de Torelli pour les intersections de trois quadriques generiques de dimension impaire.- Nodal quintics in P4.- Volumes of fundamental domains of Picard modular groups.- The siegel modular variety of degree two and level four: A report.- Some effective estimates for elliptic curves.- A pencil of K3- surfaces related to Apéry's recurrence for ?(3) and Fermi surfaces for potential zero.- The work of kolyvagin on the arithmetic of elliptic curves.- Cyclic covers of Pv branched along v + 2 hyperplanes and the generalized Hodge Conjecture for certain abelian varieties.- On the cohomology of siegel modular threefolds.