Finite Hilbert stability of (bi)canonical curves

Details Finite Hilbert stability of (bi)canonical curves Finite Hilbert stability of (bi)canonical curves

2011-09-23

arxiv.org/abs/1109.4986v2

Mathematics

Algebraic Geometry

Scientific paper

We prove that a generic smooth curve of odd genus, canonically or bicanonically embedded, has a semistable m-th Hilbert point for all m. This is accomplished by proving finite Hilbert semistability of special singular curves, a nonreduced canonically embedded curve, called the balanced ribbon, and a bicanonically embedded tacnodal curve, called the rosary. Finally, we give examples of canonically embedded curves whose m-th Hilbert points have the property that they are non-semistable for low m, but become semistable past a definite threshold value of m.

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