Construction de familles minimales de courbes gauches

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Let A be a local noetherian ring and N be a locally sheaf on the projective space P³ₐ: one proves easily that there exists a family C of (smooth connected) curves contained in P³ₐ, flat over A, and an integer h such that the ideal sheaf J of C has a resolution 0→ P→ N→ J→ 0 where P is a direct sum of invertible sheaves Oₚ(-nᵢ). In this paper we determine, for a given sheaf N, all the families of curves with such a resolution, especially the minimal ones (corresponding to the minimum value of h). It gives a description of the biliaison class related to N, and a tool for constructing families of space curves.