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 , . 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}
}