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Geometric Invariant Theory for Polarized Curves

Geometric Invariant Theory for Polarized Curves by Gilberto Bini
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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

Springer International Publishing; November 2014
217 pages; ISBN 9783319113371
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Title: Geometric Invariant Theory for Polarized Curves
Author: Gilberto Bini; Fabio Felici; Margarida Melo; Filippo Viviani
 
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