Geometric Invariant Theory for Polarized Curves

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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 3.54, the Hilbert semistable locus coincides with the Chow semistable locus ...

Geometric Invariant Theory for Polarized Curves 2014, Springer International Publishing AG, Cham

ISBN-13: 9783319113364