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Theoretical analysis demonstrates an explicit cubic fourfold connection in discriminant 24 geometry, indicating an isomorphism with the Debarre–Voisin hyperkähler fourfold.
We develop the notion of Peskine sixfolds with associated K3 surfaces and cubic fourfolds and work out numerical conditions for when these associations occur. In discriminant 24, the first family for which there is an associated cubic fourfold, we identify the cubic explicitly. Moreover, we prove that in this case the Fano variety of lines of the cubic fourfold is isomorphic to the associated Debarre–Voisin hyperkähler fourfold.
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Brooke et al. (2026) studied this question.
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