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An example on deformation of a pair
In this paper we give an example to show Clemens' conjecture is not a first
order deformation problem
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 to a generic
hypersurface of 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].Comment: arXiv admin note: substantial text overlap with arXiv:1202.283
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