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arXiv · 2603.17487

Quantum cohomology and irrationality of Gushel-Mukai fourfolds

Vladimiro Benedetti·Laurent Manivel·Nicolas Perrin
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Abstract

We compute the small quantum cohomology of Gushel-Mukai fourfolds. Following [13], our computations imply that the very general ones are not rational. Following [8], and thanks to a suitable deformation of the small quantum cohomology ring, we also deduce that a rational Gushel-Mukai fourfold has the same rational cohomology as some K3 surface.

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Vladimiro Benedetti, Laurent Manivel, Nicolas Perrin. 2026-03-18. Quantum cohomology and irrationality of Gushel-Mukai fourfolds. https://arxiv.org/abs/2603.17487

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