Resumen de Un pas vers la connexité du schéma de Hilbert: les courbes de Koszul sont dans la composante des extrémales

Daniel Perrin

• 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.