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The special Brauer group and twisted Picard varieties

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arxiv 2310.04032 v2 pith:2GPOET44 submitted 2023-10-06 math.AG

Daniel Huybrechts , Dominique Mattei This is my paper · ORCID
classification math.AG
keywords groupsurfacebrauerspecialtate-shafarevichtwistedconstructioncurves
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We generalise the notion of the Tate-Shafarevich group of an elliptic K3 surface with a section to the Tate-Shafarevich group of a K3 surface endowed with a linear system. The construction, which uses Grothendieck's special Brauer group, provides an efficient way to deal with moduli spaces of twisted sheaves supported on curves in a K3 surface.

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Cited by 4 Pith papers

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  1. The period-index problem for hyperk\"ahler manifolds

    math.AG 2024-11 conditional novelty 8.0 of 10

    For projective hyperkähler manifolds, the paper conjectures ind(α) | per(α)^{dim/2} and proves this bound for Hilbert schemes of K3 surfaces and, up to a coprimality condition, for Lagrangian-fibered hyperkähler manifolds.

  2. O'Grady's tenfolds from stable bundles on hyper-K\"ahler fourfolds

    math.AG 2024-11 conditional novelty 7.0 of 10

    A moduli-space construction realizes the Laza-Saccà-Voisin compactification and yields infinitely many new families of O'Grady's ten-dimensional hyper-Kähler manifolds.

  3. The Tate-Shafarevich group of a polarised K3 surface

    math.AG 2025-07 conditional novelty 6.0 of 10

    For a primitive polarization h on a K3 surface S, the Tate-Shafarevich group X(S,h) parametrizes exactly the Pic^0(C_η)-torsors admitting a good hyperkähler model.

  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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