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Hasse Obstructions to Rationality for Special Fourfolds
For every nonempty Hassett divisor $\mathcal C_d$ parameterizing special cubic fourfolds, we consider the quaternion class $β_d=(d/2,-3)$ in the two-torsion Brauer group. We prove that if a Hodge-general member of ${C}_d$ is rational then $β_d=0$ -- or, equivalently, that Huybrechts' twisted-K3 cond
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