Rational curves on general projective hypersurfaces
| dc.creator | Pacienza, Gianluca | |
| dc.date | 2000-10-03 | |
| dc.date | 2002-11-04 | |
| dc.date.accessioned | 2026-07-07T04:37:50Z | |
| dc.date.available | 2026-07-07T04:37:50Z | |
| dc.description | Let $k$ be an integer such that $1\leq k\leq n-5$, and $X_{2n-2-k}\subset \mathbf P^n$ a general projective hypersurface of degree $d=2n-2-k$. In this paper we prove that the only $k$-dimensional subvariety $Y$ of $X_{2n-2-k}$ having geometric genus zero is the one covered by the lines. As an immediate corollary we obtain that, for $n>5$, the general $X_{2n-3}\subset \mathbf P^n$, contains no rational curves of degree $δ>1$. | |
| dc.description | Final version to appear in the Journal of Algebraic Geometry. Exposition improved, according to referee's suggestions. 26 pages, Latex | |
| dc.identifier | https://arxiv.org/abs/math/0010037 | |
| dc.identifier | http://arxiv.org/abs/math/0010037 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60049 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Rational curves on general projective hypersurfaces | |
| dc.type | text |