Non-uniruledness results for spaces of rational curves in hypersurfaces

Abstract

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 $(n+1)/2\le d\le n-3$. 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 $d\ge e\sqrt{n}$.

Comments are welcome

References in corpus (1)

• The Kodaira dimension of spaces of rational curves on low degree hypersurfaces