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
| ISBN: | 9783319113364 |
| Publication date: | 19th November 2014 |
| Author: | Gilberto Bini, Fabio Felici, Margarida Melo, Filippo Viviani |
| Publisher: | Springer an imprint of Springer International Publishing |
| Format: | Paperback |
| Pagination: | 211 pages |
| Series: | Lecture Notes in Mathematics |
| Genres: |
Algebraic geometry |