D'autres composantes non r�duites de Hilb ?3

Obstructions to Deforming Space Curves and Non-reduced Components of the Hilbert Scheme

“…First they assumed that a general member C of W is a specialization of curves contained not in a cubic but in a surface of degree greater than three. Then they got a contradiction by using a dimension count of a certain family of curves on a quartic ( [6], [3]), or using the fact that the dimension of cohomology groups can only increase under specialization by semicontinuity ( [7]). …”

Obstructions to deforming curves on a 3-fold, II: Deformations of degenerate curves on a del Pezzo 3-fold

“…For the proof we refer to [13, Lemma 3.1] for (1) and [9, Lemma 1.10] for (2). We can also prove (1) by using the "fundamental exact sequence relating A i (C ⊂ S) and H i−1 (N C/V )" in [9].…”

“…J. O. Kleppe [8] and Ph. Ellia [2] considered Problem 1.1 for the case where V is the projective 3-space P 3 , S is a smooth cubic surface in P 3 and C is a smooth connected curve of degree d lying on S. Kleppe gave a conjecture (cf. Conjectures 5.1), which can be reformulated as follows: Conjecture 1.2.…”

Dimension des familles de courbes lisses sur une surface quartique normale de $\mathbb{P}3$

“…Dans cette section on justifie la La démonstration n'est en substance que la réécriture de celle d'Ellia dans [2]à la lumière d'un théorème de Lejeune-Jalabert et Gonzales-Springer non disponiblè a l'époque eténoncé après.…”

“…Dans [2], Ellia montre que les courbes lisses connexes de degré d et genre g tracées sur une quartiqueà points doubles appartiennentà des familles de dimensions g + 39. D'autre part, le théorème de Noether-Lefschetz entraine que toute courbe sur une quartique générale y est intersection complète.…”