# Geometric Invariant Theory for Polarized Curves (Lecture by Gilberto Bini,Fabio Felici,Margarida Melo,Filippo Viviani PDF

By Gilberto Bini,Fabio Felici,Margarida Melo,Filippo Viviani

We examine GIT quotients of polarized curves. extra in particular, we learn the GIT challenge for the Hilbert and Chow schemes of curves of measure d and genus g in a projective area of size d-g, as d decreases with appreciate to g. We end up that the 1st 3 values of d at which the GIT quotients swap are given by means of d=a(2g-2) the place a=2, 3.5, four. We exhibit that, for a>4, L. Caporaso's effects carry actual for either Hilbert and Chow semistability. If 3.5

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