Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Oller, Martí
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7163653794