Birational geometry of the moduli space of genus four curves
--Sebastian Casalaina-Martin, September 25, 2009  

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In addition to the moduli space of stable genus four curves,
there are a number of additional compactifications of the
moduli space of genus four curves that arise naturally.  In
this talk I will discuss joint work with Radu Laza where we
compare some of these spaces.  The description we obtain is
similar to that for genus three curves (work of Hyeon-Lee), as
well as to some previous results we have for the moduli space
of cubic threefolds.