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Courbes de l’espace projectif: Séries linéaires incomplètes et multisécantes. (Curves of the projective space: Incomplete linear series and multisecants). (French) Zbl 0585.14010
Consider a smooth irreducible curve \(X\subset {\mathbb{P}}^ 3\) of degree d and genus g. Surfaces of degree d-4 fail to cut out a complete linear series on X if and only if X has a (d-2)-secant line unless (d,g)\(\in \{(7,0);(7,1);(8,0)\}\).

MSC:
14C20 Divisors, linear systems, invertible sheaves
14H45 Special algebraic curves and curves of low genus
14N10 Enumerative problems (combinatorial problems) in algebraic geometry
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