2022
DOI: 10.48550/arxiv.2204.02048
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Graded Lie Algebras, Compactified Jacobians and Arithmetic Statistics

Abstract: A simply laced Dynkin diagram gives rise to a family of curves over Q and a coregular representation, using deformations of simple singularities and Vinberg theory respectively. Thorne has conjectured and partially proven a strong link between the arithmetic of these curves and the rational orbits of these representations.In this paper, we complete Thorne's picture and show that 2-Selmer elements of the Jacobians of the smooth curves in each family can be parametrised by integral orbits of the corresponding re… Show more

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