On the arithmetic of simple singularities of type E

Author: 

Romano, B
Thorne, J

Publication Date: 

16 April 2018

Journal: 

Research in Number Theory

Last Updated: 

2021-04-10T00:51:08.437+01:00

Issue: 

2

Volume: 

4

DOI: 

10.1007/s40993-018-0110-5

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<sub>6</sub>,E<sub>7</sub>, E<sub>8</sub>. 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.

Symplectic id: 

1136433

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article