Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rational curves on hypersurfaces of a projective variety   In this paper, we extend our result in [3] to hypersurfaces of any smooth
projective variety $Y$. Precisely we let $X_0$ be a generic hypersurface of $Y$
and $c_0:\mathbf P^1\to X_0$ be a generic birational morphism to its image,
i.e. $c_0\in Hom_{bir}(\mathbf P^1, X_0)$ is generic, such that (1)
$dim(X_0)\geq 3$, (2) $H^1( N_{c_0/Y})=0$. Then \begin{equation}
H^1(N_{c_0/X_0})=0. \end{equation}
  As an application we prove that the Clemens' conjecture holds for Calabi-Yau
complete intersections of dimension 3.

36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
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The categories of this paper are: eess
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
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The categories of this paper are: solv-int