  Let $X$ be an integral projective variety of codimension two, degree $d$ and
dimension $r$ and $Y$ be its general hyperplane section. The problem of lifting
generators of minimal degree $\sigma$ from the homogeneous ideal of $Y$ to the
homogeneous ideal of $X$ is studied. A conjecture is given in terms of $d$, $r$
and $\sigma$; it is proved in the cases $r=1,2,3$. A description is given of
linear systems on smooth plane curves whose dimension is almost maximal.
