The Hyperkahler Period-Index Conjecture
Statement
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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No person has examined this. Nothing here has been checked at all. say whether it holds →
construction · #1
Pieter Belmans and James Hotchkiss, using UnspecifiedThat credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.
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.
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