$E_8$ and the average size of the 3-Selmer group of the Jacobian of a pointed genus-2 curve

Abstract

We prove that the average size of the 3-Selmer group of a genus-2 curve with a marked Weierstrass point is 4.

arXiv commentAccepted version

References in corpus (6)

• Néron-Severi groups under specialization
• The geometric sieve and the density of squarefree values of invariant polynomials
• Descent via (3,3)-isogeny on Jacobians of genus 2 curves
• Most odd degree hyperelliptic curves have only one rational point
• Extension theorems for reductive group schemes
• Invariant theory of ${\bigwedge }^3(9)$ and genus 2 curves

Cited by in corpus (1)

• The average size of the 2-Selmer group of a family of non-hyperelliptic curves of genus 3