29 oct 2014 -- 12:00
sala Tricerri del Dipartimento di Matematica e Informatica "U. Dini" Firenze
Abstract.
The subject of the talk will be a collection of projective varieties that contain the moduli space $M_g$ of smooth curves of genus $g$ as a dense open subset. The main focus will be on explaining how this set of models arises in three apparently rather different contexts: as modular compactifications (generalizing the Deligne--Mumford compactification by stable curves), as GIT quotients of pluricanonnical Hilbert schemes, and via the log minimal model program in birational geometry. I will provide a bit of basic background on each of these threads and then review the parallel progress in our understanding of them.