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On the arithmetic of simple singularities of type <i>E</i>.
OAI: oai:www.repository.cam.ac.uk:1810/276417 • DOI: 10.17863/CAM.23720
Published by: Research in number theory
Abstract
An ADE Dynkin diagram gives rise to a family of algebraic curves. In this paper, we use arithmetic
invariant theory to study the integral points of the curves associated to the exceptional diagrams E 6 , E 7 ,
E 8 . These curves are non-hyperelliptic of genus 3 or 4. We prove that a positive proportion of each
family consists of curves with integral points everywhere locally but no integral points globally.