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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
##### Keywords:
complete linear series on smooth curve
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