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Geometric Invariant Theory for Polarized Curves (Lecture Notes in Mathematics) (in English)
Gilberto Bini; Fabio Felici; Margarida Melo (Author)
·
Springer
· Paperback
Geometric Invariant Theory for Polarized Curves (Lecture Notes in Mathematics) (in English) - Gilberto Bini; Fabio Felici; Margarida Melo
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Synopsis "Geometric Invariant Theory for Polarized Curves (Lecture Notes in Mathematics) (in English)"
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
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