Stability of 2nd Hilbert points of canonical curves

Details Stability of 2nd Hilbert points of canonical curves Stability of 2nd Hilbert points of canonical curves

2011-11-22

arxiv.org/abs/1111.5339v1

Mathematics

Algebraic Geometry

14 pages

Scientific paper

We establish GIT semistability of the 2nd Hilbert point of every
Gieseker-Petri general canonical curve by a simple geometric argument. As a
consequence, we obtain an upper bound on slopes of general families of
Gorenstein curves. We also explore the question of what replaces hyperelliptic
curves in the GIT quotients of the Hilbert scheme of canonical curves.

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