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arXiv · 2411.04222

Cubic fourfolds of discriminant 24 and rationality

Brendan Hassett
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Abstract

Cubic fourfolds of discriminant 24 contain special codimension-two algebraic cycles of degree 6 and self-intersection 20. Such cycles may be represented by singular scrolls or del Pezzo surfaces. A discriminant 24 cubic fourfold gives rise to a twisted surface, consisting of a degree-six K3 surface and a two-torsion element of its Brauer group. We show that the cubic fourfold is rational if the Brauer class vanishes. This yields a countably-infinite collection of new examples of rational cubic fourfolds, each of codimension two in moduli.

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Brendan Hassett. 2024-11-06. Cubic fourfolds of discriminant 24 and rationality. https://arxiv.org/abs/2411.04222

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