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 d decreases with respect to g. We prove that
the first three values of d at which the GIT quotients change are
given by d=a(2g-2) where a=2, 3.5, 4. We show that, for a>4,
L. Caporaso's results hold true for both Hilbert and Chow... more...