Title: On the arithmetic of simple singularities of type E,
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.