Non-uniruledness results for spaces of rational curves in hypersurfaces

Details Non-uniruledness results for spaces of rational curves in hypersurfaces Non-uniruledness results for spaces of rational curves in hypersurfaces

2009-01-28

arxiv.org/abs/0901.4565v2

Mathematics

Algebraic Geometry

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Scientific paper

We prove that the sweeping components of the space of smooth rational curves
in a smooth hypersurface of degree $d$ in $P^n$ are not uniruled if $(n+1)/2
\leq d \leq n-3$. We also show that for any positive integer $e$, the space of
smooth rational curves of degree $e$ in a general hypersurface of degree $d$ in
$P^n$ is not uniruled when $d \geq e \sqrt{n}$.

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