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 n are not uniruled if (n + 1)2 d n 3. We also show that for any e 1, the space of smooth rational curves of degree e in a general hypersurface of degree d in n is not uniruled roughly when d en.

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