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arxiv: 2603.17487 · v2 · pith:Z73FFM53new · submitted 2026-03-18 · 🧮 math.AG

Quantum cohomology and irrationality of Gushel-Mukai fourfolds

Vladimiro Benedetti (LJAD) , Laurent Manivel (I2M) , Nicolas Perrin (CMLS) This is my paper
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keywords cohomologygushel-mukaiquantumrationalfollowingfourfoldssmallcomputations
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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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  1. Quantum cohomology and birational geometry of Verra fourfolds

    math.AG 2026-05 unverdicted novelty 7.0

    Verra fourfolds have a distinct small quantum cohomology ring implying they are never birational to very general cubic or Gushel-Mukai fourfolds, with primitive cohomology matching a K3 surface when birational.