#
Compact moduli spaces and birational geometry

December 6 to December 10, 2004
at the

American Institute of Mathematics,
San Jose, California

organized by

Brendan Hassett and S'andor Kov'acs

## 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.

Papers arising from the workshop: