Some geometric properties of Hilbert schemes of space curves

Let $H$ be the Hilbert scheme of curves in complex projective $3$-space, with $d\ge 3$ and genus $g\le (d-2{)}^2\mathrm{/}4$. A complete, explicit description of the cone of curves and the ample cone of $H$ is given. From this, partial results on the group $(H)$ are deduced.