Arithmetic of Complex Manifolds

1. Front Matter

   Pages I-IV

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2. Surfaces on quintic threefolds associated to the Horrocks-Mumford bundle

   • Alf Bjørn Aure

   Pages 1-9

3. Curves of genus three on a general abelian threefold and the non-finite generation of the Griffiths group

   • Fabio Bardelli

   Pages 10-26

4. Sur les fonctions theta du second ordre

   • Arnaud Beauville, Olivier Debarre

   Pages 27-39

5. Une demonstration elementaire du theoreme de Torelli pour les intersections de trois quadriques generiques de dimension impaire

   • Olivier Debarre

   Pages 40-47

6. Nodal quintics in P4

   • Bert van Geemen, Jürgen Werner

   Pages 48-59

7. Volumes of fundamental domains of Picard modular groups

   • R.-P. Holzapfel

   Pages 60-88

8. The siegel modular variety of degree two and level four: A report

   • Ronnie Lee, Steven H. Weintraub

   Pages 89-102

9. Some effective estimates for elliptic curves

   • D. W. Masser, G. Wüstholz

   Pages 103-109

10. A pencil of K3- surfaces related to Apéry's recurrence for ζ(3) and Fermi surfaces for potential zero

    • C. Peters, J. Steinstra

    Pages 110-127

11. The work of kolyvagin on the arithmetic of elliptic curves

    • Karl Rubin

    Pages 128-136

12. Cyclic covers of P^v branched along v + 2 hyperplanes and the generalized Hodge Conjecture for certain abelian varieties

    • Chad Schoen

    Pages 137-154

13. On the cohomology of siegel modular threefolds

    • Rainer Weissauer

    Pages 155-170

14. Back Matter

    Pages 171-171

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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.

• Abelian variety
• Dimension
• algebraic geometry
• automorphic forms
• complex manifolds
• manifold
• moduli
• number theory

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