$2$-Selmer groups of hyperelliptic curves with marked points
$2$-Selmer groups of hyperelliptic curves with marked points
We consider the family of hyperelliptic curves over $\mathbb {Q}$ of fixed genus along with a marked rational Weierstrass point and a marked rational non-Weierstrass point. When these curves are ordered by height, we prove that the average Mordell–Weil rank of their Jacobians is bounded above by $5/2$, and that …