geometry-topology / Algebraic geometry
Huybrechts conjectured that for every Brauer class alpha on a hyperkahler variety X, the index divides the period raised to the power dim(X)/2, strengthening the usual period-index conjecture. Disproved on certain hyperkahler fourfolds, in both the K3^[2] and Kum^2 deformation types.
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Append-only history
The counterexamples come with divisibility bounds on the Hodge-theoretic index, at 2-torsion and 5-torsion, on very general hyperkahler fourfolds.
Research memory
Huybrechts conjectured that for every Brauer class alpha on a hyperkahler variety X, the index divides the period raised to the power dim(X)/2, strengthening the usual period-index conjecture. Disproved on certain hyperkahler fourfolds, in both the K3^[2] and Kum^2 deformation types.
The counterexamples come with divisibility bounds on the Hodge-theoretic index, at 2-torsion and 5-torsion, on very general hyperkahler fourfolds.
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