On the arithmetic of simple singularities of type E.
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Romano, Beth https://orcid.org/0000-0002-4480-636X
Thorne, Jack A
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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4903 Numerical and Computational Mathematics, 4904 Pure Mathematics, 49 Mathematical Sciences
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Springer Science and Business Media LLC
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Engineering and Physical Sciences Research Council (EP/N007204/1)