Points of Low Degree on Smooth Plane Curves
| dc.creator | Debarre, Olivier | |
| dc.creator | Klassen, Matthew | |
| dc.date | 1992-10-13 | |
| dc.date.accessioned | 2026-07-07T09:05:46Z | |
| dc.date.available | 2026-07-07T09:05:46Z | |
| dc.description | The purpose of this note is to provide some applications of Faltings' recent proof of S. Lang's conjecture to smooth plane curves. Let $C$ be a smooth plane curve defined by an equation of degree $d$ with integral coefficients. We show that for $d\ge 7$, the curve $C$ has only finitely many points whose field of definition has degree $\le d-2$ over $Q$, and that for $d\ge 8$, all but finitely many points of $C$ whose field of definition has degree $\le d-1$ over $Q$ arise as points of intersection of rational lines through rational points of $C$. | |
| dc.description | 8 pages, PlainTex 1.2 | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9210004 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9210004 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/149788 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Points of Low Degree on Smooth Plane Curves | |
| dc.type | text |