Toward GIT stability of syzygies of canonical curves
  We introduce the problem of GIT stability for syzygy points of canonical curves with a view toward a GIT construction of the canonical model of the moduli space of stable curves. As the first step in this direction, we prove semi-stability of the first syzygy point for a general canonical curve of odd genus. 
Anand Deopurkar, Maksym Fedorchuk, David Swinarski
math.AG