The Hyperkahler Period-Index Conjecture
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.
- Result
- Disproved(see note)
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Construction
- Field
- Algebraic geometry
- Posed by
- Daniel Huybrechts
- Year posed
- 2019
- Years open
- 7y
- Solved
- 2026-08-10
- Model
- Unspecified
- Vendor
- —
- Collaborators
- Pieter Belmans, James Hotchkiss
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 22 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
The counterexamples come with divisibility bounds on the Hodge-theoretic index, at 2-torsion and 5-torsion, on very general hyperkahler fourfolds.
What the AI did
The AI disclosure names the role precisely while leaving the model unnamed: "The starting points for this paper were two different LLM-assisted constructions of counterexamples, obtained independently by the authors. The paper is the synthesis of these constructions, with LLMs used to help with the copyediting." Two authors reaching counterexamples independently with model help is a stronger signal than either would be alone.
Verification
A preprint days old, with no independent review.
Source
- PaperarXiv