Compact moduli spaces and birational geometry

December 6 to December 10, 2004

at the

American Institute of Mathematics, Palo Alto, California

organized by

Brendan Hassett and S'andor Kov'acs

This workshop, sponsored by AIM and the NSF, 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:

The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and working sessions.

Invited participants include V. Alexeev, C. Araujo, N. Budur, A.-M. Castravet, L. Chen, A. Corti, T. de Fernex, G. Farkas, A. Gibney, S. Grushevsky, T. Gwena, P. Hacking, B. Hassett, D. Hyeon, S. Keel, J. Kollar, S. Kovacs, G. La Nave, Y. Lee, M. Lieblich, E. Markman, J. McKernan, I. Morrison, M. Olsson, A. Parker, Y. Prokhorov, N. Shepherd-Barron, K. Smith, E. Tevelev, M. van Opstall, E. Viehweg, S. Yang, and J. Zhang.

The deadline to apply for support to participate in this workshop has passed.

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