Droites en position generale dans l'espace projectif

On the Hilbert Function of General Unions of a Rational Curve and 2-Points

“…We have the following triples (d, a, ψ): (16, 1, 3), (15,2,6), (15,3,2), (14,4,5), (14,5, 2) and we exclude the triples (15,2,6) and (14,4,5) which have ψ > 3. We have the following quintuples (d, a, ψ, w, u): (16,1,3,5,4), (15,3,2,4,1), (14,5,2,3,2) for which Claim 4 holds. Now assume k = 6 and hence 1 ≤ a ≤ 4.…”

“…Since the case a = 0 is true by [16], we may assume 0 ≤ φ ≤ 3. The case φ = 0, by step (a) (it is the case ψ = 0.…”

“…Since 10 4 = 120, we need to test the following triples (d, a, φ) with 1 ≤ φ ≤ 2: (16, 2, 1), (15,4,2), (12, 9, 1), (11,11,2), (8,16,1), (7,18,2), (4,23,1), (3,25,2). (b3.3) Assume a = 9, 11.…”

“…Fix a general Y ∈ F (d, a − e − f ; 4) and a general S ∪ S ′ ⊂ H such that ♯(S) = e, ♯(S ′ ) = f and S ∩ S ′ = ∅. It is sufficient to prove that h i (I W (1, 17), (2,17), (3,17), (4,17), (5,13), (6,13), (7,13), (8,13), (9,10), (11,9), (12,9), (13,6), (14,6), (15,5), (16,5), (17,3), (9,8).…”

Postulation of General Unions of Decorated Lines

“…Hence W (r, t, a) is parametrized by an irreducible variety. Hence (as in [14] for the case a = 0) it makes sense to compute the Hilbert function of a general element of W (r, t, a). In this paper we prove the following result Theorem 1.…”