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The period-index problem for hyperk\"ahler manifolds
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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.
Forward citations
Cited by 4 Pith papers
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The period-index conjecture is false
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.
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TwistedMerge: Certified Higher-Order Diagnostics and Abstention for Model Merging
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.
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The period-index problem for hyper-K\"ahler varieties via hyperholomorphic bundles
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.
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Derived categories of Fano varieties of lines
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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