Geometric Invariant Theory for Polarized Curves
| By: | Gilberto Bini; Fabio Felici; Margarida Melo; Filippo Viviani |
| Publisher: | Springer Nature |
| Print ISBN: | 9783319113364 |
| eText ISBN: | 9783319113371 |
| Edition: | 0 |
| Copyright: | 2014 |
| Format: | Reflowable |
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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 semistability. If 3.5