Rational curves of degree at most 9 on a general quintic threefold
| dc.creator | Johnsen, Trygve | |
| dc.creator | Kleiman, Steven L. | |
| dc.date | 1995-10-30 | |
| dc.date | 1996-03-01 | |
| dc.date.accessioned | 2026-07-07T08:58:02Z | |
| dc.date.available | 2026-07-07T08:58:02Z | |
| dc.description | We prove the following form of the Clemens conjecture in low degree. Let $d\le9$, and let $F$ be a general quintic threefold in $\IP^4$. Then (1)~the Hilbert scheme of rational, smooth and irreducible curves of degree $d$ on $F$ is finite, nonempty, and reduced; moreover, each curve is embedded in $F$ with normal bundle $Ø(-1)\oplusØ(-1)$, and in $\IP^4$ with maximal rank. (2)~On $F$, there are no rational, singular, reduced and irreducible curves of degree $d$, except for the 17,601,000 six-nodal plane quintics (found by Vainsencher). (3)~On $F$, there are no connected, reduced and reducible curves of degree $d$ with rational components. | |
| dc.description | 31 pages, minor revisions -- current 2/29/96, Plain Tex | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9510015 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9510015 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/147165 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14J30 (primary) 14H45, 14N10 (Secondary) | |
| dc.title | Rational curves of degree at most 9 on a general quintic threefold | |
| dc.type | text |