Average size of 2-Selmer groups of Jacobians of hyperelliptic curves over function fields

Abstract

In this paper, we are going to compute the average size of 2-Selmer groups of two families of hyperelliptic curves with marked points over function fields. The result will be obtained by a geometric method which could be considered as a generalization of the one that was used previously by Q.P. Ho, V.B. Le Hung, and B.C. Ngo to obtain the average size of 2-Selmer groups of elliptic curves.

References in corpus (9)

• Squarefree values of multivariable polynomials
• The average size of the 2-Selmer group of Jacobians of hyperelliptic curves having a rational Weierstrass point
• Holomorphic principal bundles over elliptic curves
• The average size of the 5-Selmer group of elliptic curves is 6, and the average rank is less than 1
• Most hyperelliptic curves over Q have no rational points
• Average size of the 2-Selmer group of Jacobians of monic even hyperelliptic curves
• The average number of elements in the 4-Selmer groups of elliptic curves is 7
• Maximal linear spaces contained in the base loci of pencils of quadrics
• 2-Selmer groups of hyperelliptic curves with two marked points

Cited by in corpus (1)

• The geometric average size of Selmer groups over function fields