  We discuss GIT for canonically embedded genus four curves and the connection
to the Hassett-Keel program. A canonical genus four curve is a complete
intersection of a quadric and a cubic, and, in contrast to the genus three
case, there is a family of GIT quotients that depend on a choice of
linearization. We discuss the corresponding VGIT problem and show that the
resulting spaces give the final steps in the Hassett-Keel program for genus
four curves.
