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

Alf Bjørn Aure (auth.), Wolf-P. Barth, Herbert Lange (eds.)3540517294, 9783540517290

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.

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Table of contents :
Surfaces on quintic threefolds associated to the Horrocks-Mumford bundle….Pages 1-9
Curves of genus three on a general abelian threefold and the non-finite generation of the Griffiths group….Pages 10-26
Sur les fonctions theta du second ordre….Pages 27-39
Une demonstration elementaire du theoreme de Torelli pour les intersections de trois quadriques generiques de dimension impaire….Pages 40-47
Nodal quintics in P 4 ….Pages 48-59
Volumes of fundamental domains of Picard modular groups….Pages 60-88
The siegel modular variety of degree two and level four: A report….Pages 89-102
Some effective estimates for elliptic curves….Pages 103-109
A pencil of K3- surfaces related to Apéry’s recurrence for ζ(3) and Fermi surfaces for potential zero….Pages 110-127
The work of kolyvagin on the arithmetic of elliptic curves….Pages 128-136
Cyclic covers of P v branched along v + 2 hyperplanes and the generalized Hodge Conjecture for certain abelian varieties….Pages 137-154
On the cohomology of siegel modular threefolds….Pages 155-170