A duality theorem for divisors on certain algebraic curves

For the general ruled cubic surface S (with a double line) in P3 = P3 sub k, k any algebraically closed field, we find necessary conditions for which curves on S can be the specialization of a flat family of curves on smooth cubics. In particular, no smooth curve of degree > 10 on S is such a specialization.

Genera of curves varying in a family

A. Nobile (1987)

Annales scientifiques de l'École Normale Supérieure

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Curves of $g_{d}^{1,} s$

George R. Kempf (1985)

Compositio Mathematica

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