  We investigate GIT quotients of polarized curves. More specifically, we study
the GIT problem for the Hilbert and Chow schemes of curves of degree d and
genus g in a projective space of dimension d-g, as the ratio v:=d/(2g-2)
decreases. We prove that the first three values of v at which the GIT quotients
change are given by v=4, 3.5, 2. We show that, for v>4, L. Caporaso's results
hold true for both Hilbert and Chow semistability. If 3.5<v<4, the Hilbert
semistable locus coincides with the Chow semistable locus and it maps to the
moduli stack of weakly-pseudo-stable curves. If 2<v<3.5, the Hilbert and Chow
semistable loci coincide and they map to the moduli stack of pseudo-stable
curves. We also analyze in detail the critical values v=3.5 and v=4, where the
Hilbert semistable locus is strictly smaller than the Chow semistable locus. As
an application, we obtain three compactifications of the universal Jacobian
over the moduli space of stable curves, weakly-pseudo-stable curves and
pseudo-stable curves, respectively.
