arXiv:2610.40811v1 Announce Type: new Abstract: Following the recent work by OpenAI on the irrationality of very general cubic fourfolds in Hassett divisors, we prove some compatibility of Iritani's blow-up formula with the classical blow-up decomposition of integral Hodge structures. As a consequence, we express OpenAI's birational invariant in terms of the theory of atoms developped by Katzarkov--Kontsevich--Pantev--Yu. We also show that, for every smooth complex rational cubic fourfold, the primitive cohomology is isometric as an integral Hodge structure to the twisted middle cohomology of a K3 surface and we prove irrationality of the very general Verra fourfold.
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