A-periods of non-commutative resolutions of Calabi-Yau double covers satisfy the same GKZ system as those of an explicitly constructed smooth complete intersection.
Derived Equivalent Calabi-Yau 3-folds from Cubic 4-folds
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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.
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Non-commutative resolutions and pre-quotients of Calabi-Yau double covers
A-periods of non-commutative resolutions of Calabi-Yau double covers satisfy the same GKZ system as those of an explicitly constructed smooth complete intersection.