The derived category of the Fano variety of lines of a smooth cubic fourfold is equivalent to the symmetric square of its Kuznetsov component, proving Galkin's conjecture.
The Pfaffian-Grassmannian equivalence revisited
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abstract
We give a new proof of the 'Pfaffian-Grassmannian' derived equivalence between certain pairs of non-birational Calabi-Yau threefolds. Our proof follows the physical constructions of Hori and Tong, and we factor the equivalence into three steps by passing through some intermediate categories of (global) matrix factorizations. The first step is global Knoerrer periodicity, the second comes from a birational map between Landau-Ginzburg B-models, and for the third we develop some new techniques.
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The Fano of lines, the Kuznetsov component, and a flop
The derived category of the Fano variety of lines of a smooth cubic fourfold is equivalent to the symmetric square of its Kuznetsov component, proving Galkin's conjecture.