Points of Low Degree on Smooth Plane Curves

Details Points of Low Degree on Smooth Plane Curves Points of Low Degree on Smooth Plane Curves

1992-10-13

arxiv.org/abs/alg-geom/9210004v1

Mathematics

Algebraic Geometry

8 pages, PlainTex 1.2

Scientific paper

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 $C$.

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