Nonuniruledness results for spaces of rational curves in hypersurfaces

Beheshti, Roya

doi:10.2140/ant.2012.6.669

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Nonuniruledness results for spaces of rational curves in hypersurfaces

Roya Beheshti

Vol. 6 (2012), No. 4, 669–687

DOI: 10.2140/ant.2012.6.669

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

Keywords

rational curves on hypersurfaces

Mathematical Subject Classification 2010

Primary: 14J70

Secondary: 14J40, 14E05

Milestones

Received: 20 September 2010

Revised: 19 June 2011

Accepted: 28 July 2011

Published: 25 July 2012

Authors

Roya Beheshti
Department of Mathematics Washington University Campus Box 1146 Saint Louis, MO 63130 United States

Vol. 6, No. 4, 2012