Orbits on tri-involutive K3 surfaces

Abstract: Let $\mathcal W$ be a surface in $\mathbb P^1 \times \mathbb P^1 \times \mathbb P^1$ given by the vanishing of a (2,2,2) form. The three projections $\mathcal W \to \mathbb P^1 \times \mathbb P^1$ are double covers that induce three non-commuting involutions on $\mathcal W.$ Let $G$ be the group of automorphisms of $\mathcal W$ generated by these involutions. We investigate the $G$-orbit structure of the points of $\mathcal W$. In particular, we study $G$-orbital components over finite fields and finite $G$-orbits in characteristic 0. This is joint work with Elena Fuchs, Matthew Litman, and Austin Tran.

number theory

Audience: researchers in the topic

Columbia CUNY NYU number theory seminar