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

Daniel Perrin (2001)

Collectanea Mathematica

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.

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