On the arithmetic of simple singularities of type E

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 [Formula: see text] , [Formula: see text] . These curves are non-hyperelliptic of genus 3 or 4. We pro...

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Detalles Bibliográficos
Autores principales: Romano, Beth, Thorne, Jack A.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6428336/
https://www.ncbi.nlm.nih.gov/pubmed/30957001
http://dx.doi.org/10.1007/s40993-018-0110-5
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author Romano, Beth
Thorne, Jack A.
author_facet Romano, Beth
Thorne, Jack A.
author_sort Romano, Beth
collection PubMed
description 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 [Formula: see text] , [Formula: see text] . 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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spelling pubmed-64283362019-04-05 On the arithmetic of simple singularities of type E Romano, Beth Thorne, Jack A. Res Number Theory Research 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 [Formula: see text] , [Formula: see text] . 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. Springer International Publishing 2018-04-16 2018 /pmc/articles/PMC6428336/ /pubmed/30957001 http://dx.doi.org/10.1007/s40993-018-0110-5 Text en © The Author(s) 2018 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Romano, Beth
Thorne, Jack A.
On the arithmetic of simple singularities of type E
title On the arithmetic of simple singularities of type E
title_full On the arithmetic of simple singularities of type E
title_fullStr On the arithmetic of simple singularities of type E
title_full_unstemmed On the arithmetic of simple singularities of type E
title_short On the arithmetic of simple singularities of type E
title_sort on the arithmetic of simple singularities of type e
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6428336/
https://www.ncbi.nlm.nih.gov/pubmed/30957001
http://dx.doi.org/10.1007/s40993-018-0110-5
work_keys_str_mv AT romanobeth onthearithmeticofsimplesingularitiesoftypee
AT thornejacka onthearithmeticofsimplesingularitiesoftypee

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