#
Log minimal model program for moduli spaces

December 10 to December 14, 2012
at the

American Institute of Mathematics,
Palo Alto, California

organized by

Jarod Alper,
Maksym Fedorchuk,
Brendan Hassett,
and David Smyth

## Original Announcement

This workshop will be devoted to applications of the minimal model program (MMP) to the study of geometry of moduli spaces of algebraic varieties.
A fundamental problem in algebraic geometry is the problem of constructing a moduli space for a nice class of varieties (e.g. smooth curves, smooth polarized K3 surfaces) and of finding a geometrically meaningful compactification for this moduli space. Once a compactification is constructed, one applies the methods of deformation theory and projective geometry to study, respectively, the local and the global geometry of the moduli space. Compactifications of moduli spaces of smooth objects can be constructed using different methods, including stack-theoretic methods, Geometric Invariant Theory (GIT), and the MMP. The principal focus of the workshop will be to use the minimal model program as a framework for understanding the relationships between these different compactifications.

More specifically, the main topics for the workshop are:

- The minimal model program for the moduli space of stable curves and stable maps; in particular, the search for a modular interpretation of the log canonical models of the moduli space of stable curves.
- Geometric Invariant Theory of polarized varieties; especially, stability of Hilbert points of pluricanonically embedded curves and surfaces.
- Extending recently developed techniques in moduli theory of curves to construct and study geometrically meaningful compactifications of moduli spaces of surfaces.

An important goal of the workshop will be to consolidate and disseminate the variety of different techniques, heuristics, and approaches that has been applied to these problems in recent years.

## Material from the workshop

A list of participants.
The workshop schedule.

A report on the workshop activities.