Vol. 6, No. 4, 2012

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Nonuniruledness results for spaces of rational curves in hypersurfaces

Roya Beheshti

Vol. 6 (2012), No. 4, 669–687
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 $\left(n+1\right)∕2\le d\le n-3$. We also show that for any $e\ge 1$, the space of smooth rational curves of degree $e$ in a general hypersurface of degree $d$ in ${ℙ}^{n}$ is not uniruled roughly when $d\ge e\sqrt{n}$.

Keywords
rational curves on hypersurfaces
Mathematical Subject Classification 2010
Primary: 14J70
Secondary: 14J40, 14E05