Title: The geometry of spaces of rational curves on hypersurfaces
Abstract: (From the corresponding preprint --
but may not correspond exactly to the talk)
``We prove that the sweeping components of the space of smooth rational curves
in a smooth hypersurface of degree d in Pn are not uniruled if
(n + 1)/2 <= d <= n - 3. We also show that for any e >= 1, the space of smooth
rational curves of degree e in a general hypersurface of degree d in P^n is not
uniruled when d >= e\sqrt(n).''