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arXiv · 1707.04355

On the arithmetic of simple singularities of type E

Beth Romano·Jack A. Thorne
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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.

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Beth Romano, Jack A. Thorne. 2017-07-13. On the arithmetic of simple singularities of type E. https://arxiv.org/abs/1707.04355

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