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 E<sub>6</sub>,E<sub>7</sub>, E<sub>8</sub>. These curves are non-h...
Main Authors: | , |
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Format: | Journal article |
Language: | English |
Published: |
Springer
2018
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Summary: | 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. |
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