Beth Romano

activity

20172019

collaborators

3 papers

math.RT2019

On central extensions and simply laced Lie algebras

Beth Romano

Let $Λ$ be a simply laced root lattice and $w$ an elliptic automorphism of $Λ$ of order $d$ . This paper gives a construction that begins with a central extension of the group of co…

math.NT2018

$E_{8}$ and the average size of the 3-Selmer group of the Jacobian of a pointed genus-2 curve

Beth Romano, Jack A. Thorne

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

math.NT2017

On the arithmetic of simple singularities of type E

Beth Romano, Jack A. Thorne

An ADE Dynkin diagram gives rise to a family of algebraic curves. In this paper, we use arithmetic invariant theory to study the integral points of the curves associated to the exc…

On central extensions and simply laced Lie algebras

E8​ and the average size of the 3-Selmer group of the Jacobian of a pointed genus-2 curve

On the arithmetic of simple singularities of type E

$E_{8}$ and the average size of the 3-Selmer group of the Jacobian of a pointed genus-2 curve