English

On the arithmetic of simple singularities of type E

Number Theory 2017-07-17 v1

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 E6,E7E_6, E_7, E8E_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.

Keywords

Cite

@article{arxiv.1707.04355,
  title  = {On the arithmetic of simple singularities of type E},
  author = {Beth Romano and Jack A. Thorne},
  journal= {arXiv preprint arXiv:1707.04355},
  year   = {2017}
}
R2 v1 2026-06-22T20:46:45.384Z