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The period-index problem for hyperk\"ahler manifolds

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arxiv 2411.17604 v2 pith:D3A5TR4Z submitted 2024-11-26 math.AG

classification math.AG
keywords ahlerhyperkalphamanifoldsprojectivetextconjectureadmitting
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abstract

We conjecture that every unramified Brauer class $\alpha\in \text{Br}(X)$ on a projective hyperk\"ahler manifold $X$ satisfies $\text{ind}(\alpha)\mid\text{per}(\alpha)^{\dim(X)/2}$. We provide evidence for this conjecture by proving it for two large classes of projective hyperk\"ahler manifolds: For projective hyperk\"ahler manifolds admitting a Lagrangian fibration and for Hilbert schemes of K3 surfaces.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The period-index conjecture is false

    math.AG 2026-08 accept novelty 8.0 of 10

    The period-index conjecture is disproved: for every d≥3 there is a variety with a 2-torsion Brauer class of index 2^{d-1}, exceeding the conjectural bound.

  2. TwistedMerge: Certified Higher-Order Diagnostics and Abstention for Model Merging

    cs.LG 2026-07 conditional novelty 6.0 of 10

    Cycle inconsistency in model merging is not automatically a cohomological obstruction: TwistedMerge certifies a class only after frozen-complex, centrality, closure, and statistical gates, and finds no natural central class.

  3. The period-index problem for hyper-K\"ahler varieties via hyperholomorphic bundles

    math.AG 2025-02 accept novelty 6.0 of 10

    For K3^{[n]}-type hyper-Kähler varieties, the index of a Brauer class divides a power of its period, with exponent equal to the dimension in general and half the dimension for most classes in Picard rank at least two.

  4. Derived categories of Fano varieties of lines

    math.AG 2025-01 conditional novelty 6.0 of 10

    Proves Galkin's derived-equivalence conjecture for generic cubic fourfolds in Hassett divisors with d/2 a perfect square, and establishes the associated weight-two Hodge isometry for all smooth cubic fourfolds.

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