November 30, 2025Journal de Théorie des Nombres de BordeauxOpen Access

The density of ADE families of curves having squarefree discriminant

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Density of curves with squarefree discriminant found to be product of local densities,
Key evidence shows density calculated across specific families arising from Vinberg representations.
Analysis using orbit-counting techniques demonstrates methodological robustness and application.
Findings suggest broader implications for understanding dimensional properties in algebraic geometry.

Implication

Assessment reveals density of curves with squarefree discriminant in ADE families, indicating global density equals local densities.

Abstract

We determine the density of curves having squarefree discriminant in some families of curves that arise from Vinberg representations, showing that the global density is the product of the local densities. We do so using the framework of Thorne and Laga’s PhD theses and Bhargava’s orbit -counting techniques. This paper generalises a previous result by Bhargava, Shankar and Wang.

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A 2025 study studied this question.

synapsesocial.com/papers/692b9d931d383f2b2a379e6e https://doi.org/10.5802/jtnb.1349

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Implication

Assessment reveals density of curves with squarefree discriminant in ADE families, indicating global density equals local densities.

The density of ADE families of curves having squarefree discriminant

Key Points

Implication

Abstract

Discussion

Cite This Study

The density of ADE families of curves having squarefree discriminant

Key Points

Implication

Abstract

Discussion

Cite This Study

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