Equivalence of K3 surfaces from Verra threefolds

TL;DR

This paper investigates special pairs of K3 surfaces derived from Verra threefolds, confirming their existence and properties predicted by prior theoretical work, and explores their geometric and algebraic relationships.

Contribution

It demonstrates the existence of non-isomorphic, derived equivalent, and L-equivalent K3 surface pairs from (2,2) divisors in P^2×P^2, confirming predictions by Kuznetsov and Shinder.

Findings

Existence of such K3 pairs confirmed.

Pairs are non-isomorphic but derived and L-equivalent.

Supports theoretical predictions about Verra threefolds.

Abstract

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