arXiv subjects

Martí Oller

Publications and source records attributed to Martí Oller.

3 recordsLinked to original sources

arXiv2026

Arithmetic statistics of isogeny Selmer groups associated to hyperelliptic curves

We determine asymptotic results for the average size of Selmer groups arising from certain isogenies related to Jacobians of hyperelliptic curves of genus $g\geq 2$. Our results come from two different routes. The first route is through the geometry-of-numbers methods pioneered by Bhargava, where we obtain new parametrisations coming from Vinberg theory arising from representations related to the Dynkin diagrams of type $B$ and $C$. The second route uses recent results by Koymans--Smith, which relate the average sizes of Selmer groups to Tamagawa ratios through a formula by Greenberg--Wiles.

math.NT↗

arXiv2025

The density of ADE families of curves having squarefree discriminant

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. As an application, we give an asymptotic for the number of reducible orbits of our representations.

math.NT↗

arXiv2025

Geometry-of-numbers over number fields and the density of ADE families of curves having squarefree discriminant

For families of curves arising from a Dynkin diagram of type ADE, we show that the density of such curves having squarefree discriminant is equal to the product of local densities. We do so using the framework of Thorne and Laga's PhD theses and geometry-of-numbers techniques developed by Bhargava, here expanded over number fields.

math.NT↗