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Article Dans Une Revue Journal of Algebraic Geometry Année : 2003

Rational curves on general projective hypersurfaces

Gianluca Pacienza
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Résumé

Let $k$ be an integer such that $1\leq k\leq n-5$, and $X_{2n-2-k}\subset \mathbf P^n$ a general projective hypersurface of degree $d=2n-2-k$. In this paper we prove that the only $k$-dimensional subvariety $Y$ of $X_{2n-2-k}$ having geometric genus zero is the one covered by the lines. As an immediate corollary we obtain that, for $n>5$, the general $X_{2n-3}\subset \mathbf P^n$, contains no rational curves of degree $\delta >1$.

Dates et versions

hal-00127009 , version 1 (27-01-2007)

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Gianluca Pacienza. Rational curves on general projective hypersurfaces. Journal of Algebraic Geometry, 2003, 12, pp.245-267. ⟨hal-00127009⟩
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