Moduli of Curves and Abelian Varieties

The present volume, with contributions of R. Dijkgraaf, C. Faber, G. van der Geer, R. Rain, E. Looijenga, and F. Oort, originates from the Dutch Intercity Seminar on Moduli (year 1995-96). Some of the articles here were discussed, in preliminary form, in the seminar; others are completely new. Two introductory papers, on moduli of abelian varieties and on moduli of curves, accompany the articles. Topics include a stratification of a moduli space of abelian varieties in positive characteristic, and the calculation of the classes of the strata, tautological classes for moduli of abelian varieties as well as for moduli of curves, correspondences between moduli spaces of curves, locally symmetric families of curves and jaco bians, and the role of symmetric product spaces in quantum field theory, string theory and matrix theory. This Intercity Seminar is part of the long term project "Algebraic curves and Riemann surfaces: geometry, arithmetic and applications" , sponsored hy the Netherlands Organization for Scientific Research (NWO), that has been running since 1994. Its ancestry can be traced back to joint activities in the seventies (if not earlier), which as of 1980 had evolved into active biweekly research seminars. These have been a focal point of Dutch algebraic geometry and singularity theory since. We are grateful to NWO for its support for the project. C.F. thanks the Max-Planck-Institut fur Mathematik, Bonn, for support during the final stages of the preparation of this volume.