d’Almeida, Jean Courbes de l’espace projectif: Séries linéaires incomplètes et multisécantes. (Curves of the projective space: Incomplete linear series and multisecants). (French) Zbl 0585.14010 J. Reine Angew. Math. 370, 30-51 (1986). 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)\(\in \{(7,0);(7,1);(8,0)\}\). Cited in 1 ReviewCited in 11 Documents 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 PDFBibTeX XMLCite \textit{J. d'Almeida}, J. Reine Angew. Math. 370, 30--51 (1986; Zbl 0585.14010) Full Text: DOI EuDML