Finite Hilbert stability of canonical curves, II. The even-genus case
Algebraic Geometry
2011-10-28 v1
Abstract
This paper is a sequel to arXiv:1109.4986, where we proved that a general smooth curve of odd genus, canonically or bicanonically embedded, has semistable finite Hilbert points. Here, we prove that a generic canonically embedded curve of even genus has semistable finite Hilbert points. More precisely, we prove that a generic canonically embedded trigonal curve of even genus has semistable finite Hilbert points. Furthermore, we show that the analogous result fails for bielliptic curves. Namely, the Hilbert points of bielliptic curves are asymptotically semistable but become non-semistable below a definite threshold value depending on genus.
Keywords
Cite
@article{arxiv.1110.5960,
title = {Finite Hilbert stability of canonical curves, II. The even-genus case},
author = {Jarod Alper and Maksym Fedorchuk and David Ishii Smyth},
journal= {arXiv preprint arXiv:1110.5960},
year = {2011}
}