  The aim of this note is to announce some results on the GIT problem for the
Hilbert and Chow scheme of curves of degree d and genus g in P^{d-g}, whose
full details will appear in a subsequent paper. In particular, we extend the
previous results of L. Caporaso up to d>4(2g-2) and we observe that this is
sharp. In the range 2(2g-2)<d<7/2(2g-2), we get a complete new description of
the GIT quotient. As a corollary, we get a new compactification of the
universal Jacobian over the moduli space of pseudo-stable curves.
