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The D-equivalence conjecture for hyper-K\"ahler varieties via hyperholomorphic bundles

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arxiv 2408.14775 v5 pith:YZ2RZBYI submitted 2024-08-27 math.AG

classification math.AG
keywords ahlerconjectured-equivalencehyper-kvarietiesbundlesderivedhyperholomorphic
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abstract

We show that birational hyper-K\"ahler varieties of $K3^{[n]}$-type are derived equivalent, establishing the D-equivalence conjecture in these cases. The Fourier-Mukai kernels of our derived equivalences are constructed from projectively hyperholomorphic bundles, following ideas of Markman. Our method also proves a stronger version of the D-equivalence conjecture for hyper-K\"ahler varieties of $K3^{[n]}$-type with Brauer classes.

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Cited by 2 Pith papers

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

  1. 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.

  2. 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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