geometry-topology / Algebraic geometry

The Hyperkahler Period-Index Conjecture

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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geometry-topologyAug 10, 2026Significance 22/100Registry: unreviewed

The Hyperkahler Period-Index Conjecture

Prior state unknown→disproved

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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The counterexamples come with divisibility bounds on the Hodge-theoretic index, at 2-torsion and 5-torsion, on very general hyperkahler fourfolds.

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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The Hyperkahler Period-Index Conjecture — Mathematical Frontier Network