Compact moduli spaces and birational geometry

December 6 to December 10, 2004

at the

American Institute of Mathematics, Palo Alto, California

organized by

Original Announcement

This workshop will be devoted to the study of compact moduli spaces, especially those inspired by the minimal model program. Perhaps the first example is the Deligne/Mumford compactification of the moduli space of stable curves, where the limiting curves are dictated by the structure of canonical models for surfaces fibered over curves. This was extended to surfaces by Koll'ar/Shepherd-Barron and Alexeev, which led to work of Corti, Hacking, Tevelev/Keel, Alexeev, and others, where birational geometry inspired the choice of limiting objects, and sometimes played a role in constructing moduli spaces.

At the same time, moduli spaces themselves have increasingly been studied as birational objects. The work of Gibney, Keel, McKernan, and Ian Morrison makes clear that the inductive structure on the boundary strata of the moduli spaces of pointed stable curves has profound implications for their birational geometry. However, the successful computation of canonical models for moduli spaces of abelian varieties only highlights how much remains elusive about the curve case.

The main goals of this workshop are: to promote cross-fertilization by bringing together specialists in birational geometry and moduli theory; to make the techniques of the field more widely-known and accessible; and to identify concrete, tractable questions for young researchers entering the area.

The main topics for the workshop are:

Birational geometry of moduli spaces of curves and abelian varieties
Geometric compactifications inspired by the minimal model program
New approaches to compact moduli for surfaces

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

A list of open problems.