The purpose of this paper is to study the connectedness of the Hilbert scheme H(d,g) of degree d and genus g curves (locally Cohen-Macaulay) in P3. Thanks to the method of triads, we show that a large class of curves (the curves whose Rao-module is Koszul, i.e. a complete intersection) are in the connected component of extremal curves. This generalizes widely several recent results.
@article{urn:eudml:doc:42802,
title = {Un pas vers la connexit\'e du sch\'ema de Hilbert: les courbes de Koszul sont dans la composante des extr\'emales.},
journal = {Collectanea Mathematica},
volume = {52},
year = {2001},
pages = {295-319},
zbl = {1074.14500},
mrnumber = {MR1885224},
language = {fr},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:42802}
}
Perrin, Daniel. Un pas vers la connexité du schéma de Hilbert: les courbes de Koszul sont dans la composante des extrémales.. Collectanea Mathematica, Tome 52 (2001) pp. 295-319. http://gdmltest.u-ga.fr/item/urn:eudml:doc:42802/