Moduli spaces of singular curves via GIT for canonical curves
-- Maksym Fedorchuk, September 30, 2011

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We will describe a proof of semistability of finite Hilbert
points for the general canonical curve of arbitrary genus
(this is joint work with Jarod Alper and David Smyth).  The
generic stability result opens the door to analyzing a whole
menagerie of new GIT quotients, which are expected to be log
canonical models of the moduli space of stable curves. In low
genus this expectation can be verified, and a complete GIT
analysis is possible.  We will discuss two instances of such an
analysis leading to a functorial description of the final log
canonical models of the moduli spaces of stable curves of genus 4
and 5.