Equivalence of K3 surfaces from Verra threefolds

Abstract

We study $(2,2)$ divisors in ${\mathbb{P}}^2\times {\mathbb{P}}^2$ giving rise to pairs of nonisomorphic, derived equivalent, and $\mathbb{L}$-equivalent K3 surfaces of degree $2$. In particular, we confirm the existence of such fourfolds as predicted recently by Kuznetsov and Shinder.