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Obstruction classes for moduli spaces of sheaves and Lagrangian fibrations

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arxiv 2404.16652 v2 pith:3XJDXXZX submitted 2024-04-25 math.AG

Dominique Mattei , Reinder Meinsma This is my paper · ORCID
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keywords moduliobstructionsurfacesbeauville-mukaibrauerclassesequivalencesgroup
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We investigate obstruction classes of moduli spaces of sheaves on K3 surfaces. We extend previous results by Caldararu, explicitly determining the obstruction class and its order in the Brauer group. Our main theorem establishes a short exact sequence relating the Brauer group of the moduli space to that of the underlying K3 surface. This provides a criterion for when the moduli space is fine, generalising well-known results for K3 surfaces. Additionally, we explore applications to Ogg-Shafarevich theory for Beauville-Mukai systems. Furthermore, we investigate birational equivalences of Beauville-Mukai systems on elliptic K3 surfaces, presenting a complete characterisation of such equivalences.

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  1. 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.

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