Derived Equivalent Calabi-Yau 3-folds from Cubic 4-folds

TL;DR

This paper constructs examples of derived equivalences between Calabi-Yau threefolds originating from special cubic fourfolds with associated K3 surfaces, revealing new relationships in algebraic geometry.

Contribution

It introduces a novel method to produce derived equivalent Calabi-Yau threefolds from pencils of cubic fourfolds with special properties.

Findings

Derived equivalent Calabi-Yau threefolds from cubic fourfolds

Explicit examples of autoequivalences of Calabi-Yau threefolds

Connections between cubic fourfolds, K3 surfaces, and Calabi-Yau geometry

Abstract

We describe pretty examples of derived equivalences and autoequivalences of Calabi-Yau threefolds arising from pencils of cubic fourfolds. The cubic fourfolds are chosen to be special, so they have an associated K3 surface. Thus a pencil gives rise to two different Calabi-Yau threefolds: the associated pencil of K3 surfaces, and the baselocus of the original pencil - the intersection of two cubic fourfolds. They both have crepant resolutions which are derived equivalent.