Rational curves on hypersurfaces
  In this paper, we prove three related results;   (1) Extension of our result in [10] to all generic hypersurfaces. More precisely, the normal sheaf of a generic rational map $c_0$ to a generic hypersurface $X_0$ of $\mathbf P^n, n\geq 4$ has a vanishing higher cohomology, \begin{equation} H^1(N_{c_0/X_0})=0. \end{equation}   As applications we give   (2) A solution to a Voisin's conjecture [9] on a covering of a generic hypersurface by rational curves   (3) A classification of rational curves on hypersurfaces of general type--a solution to another Voisin's conjecture [9]. 
Bin Wang
math.AG