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arXiv · 2603.04518

On the irrationality of cubic fourfolds

Jérémy Guéré
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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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Jérémy Guéré. 2026-03-04. On the irrationality of cubic fourfolds. https://arxiv.org/abs/2603.04518

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