Moduli of Curves and Abelian Varieties

The Dutch Intercity Seminar on Moduli, which dates back to the early
eighties, was an initiative of G. van der Geer, F. Oort and C. Peters.
Through the years it became a focal point of Dutch mathematics and
it gained some fame, also outside Holland, as an active biweekly
research seminar. The tradition continues up to today.
The present volume, with contributions of R. Dijkgraaf, C. Faber,
G. van der Geer, R. Hain, E. Looijenga, and F. Oort, originates
from the seminar held in 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 jacobians, and the role of
symmetric product spaces in quantum field theory, string theory and
matrix theory.

Autorentext

Prof. Dr. Eduard Looijenga ist Mathematiker an der Universität Utrecht, Niederlande.

Dr. Carel Faber ist jetzt am Max-Planck-Institut für Mathematik in Bonn tätig.

Inhalt

• Gerard van der Geer / Frans Oort: Moduli of Abelian Varieties: A Short Introduction and Survey. - Carel Faber/ Eduard Looijenga: Remarks on Moduli of Curves. - Robbert Dijkgraaf: Fields, Strings, Matrices and Symmetric Products. - Carel Faber: A Conjectural Description of the Tautological Ring of the Moduli Space of Curves. - Gerard van der Geer: Cycles on the Moduli Space of Abelian Varieties. - Richard Hain: Locally Symmetric Families of Curves and Jacobians. - Eduard Looijenga: Correspondences between Moduli Spaces of Curves. - Frans Oort: A Stratification of a Moduli Space of Polarized Abelian Varieties in Positive Characteristic.