8 oct 2014 -- 15:00
Aula Magna, DM, Pisa
Seminario di Geometria, Pisa
Abstract.
The moduli space $\overline{M}_g$ of stable curves of genus $g$ has proven a fruitful test case for general questions from the minimal model program in birational geometry, where its modular interpretation provides extra tools for answering these questions. A paradoxical aspect of this work is that, although the questions deal with the intrinsic geometry of $\overline{M}_g$, constructing the models depends on interpreting them as alternate compactifications of $M_g$, and, until very recently, on extrinsic constructions of them as GIT quotients. I will review the history of these interactions and the parallel progress in our understanding of these three threads.