Zero cycles on generic hypersurfaces of large degree
  We show that given a smooth projective variety X over C with dim(X) > 2, an ample line bundle O(1) on X and an integer n > 1, any n distinct points on a generic hypersurface of degree d in X are linearly independent in CH_0(X) if d >> 0. This generalizes a result of C. Voisin. 
Najmuddin Fakhruddin