On the irrationality of cubic fourfolds
Abstract
Following the work of Katzarkov--Kontsevich--Pantev--Yu concerning the irrationality of the very general complex cubic fourfold, we prove the following: for every rational smooth complex cubic fourfold, the primitive cohomology is isomorphic as a Hodge structure to the (twisted) middle cohomology of a projective K3 surface.
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