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An analogue of Liouville’s Theorem and an application to cubic surfaces

Research paper by David McKinnon, Mike Roth

Indexed on: 18 Aug '16Published on: 02 Aug '16Published in: European Journal of Mathematics



Abstract

Abstract We prove a strong analogue of Liouville’s Theorem in Diophantine approximation for points on arbitrary algebraic varieties. We use this theorem to prove a conjecture of the first author for cubic surfaces in \(\mathbb {P}^3\) .AbstractWe prove a strong analogue of Liouville’s Theorem in Diophantine approximation for points on arbitrary algebraic varieties. We use this theorem to prove a conjecture of the first author for cubic surfaces in \(\mathbb {P}^3\) . \(\mathbb {P}^3\) \(\mathbb {P}^3\)