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Stability conditions on Kuznetsov components

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arxiv 1703.10839 v5 pith:IB6E7DS3 submitted 2017-03-31 math.AG

Arend Bayer , Martí Lahoz , Emanuele Macrì , Paolo Stellari This is my paper · ORCID
classification math.AG
keywords conditionsstabilitybridgelandcomponentscubicfourfoldskuznetsovappendix
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We introduce a general method to induce Bridgeland stability conditions on semiorthogonal components of triangulated categories. In particular, we prove the existence of Bridgeland stability conditions on the Kuznetsov component of the derived category of Fano threefolds and of cubic fourfolds. As an application, in the appendix, written jointly with Xiaolei Zhao, we give a variant of the proof of the Torelli theorem for cubic fourfolds by Huybrechts and Rennemo.

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  1. The hyper-Kummer construction

    math.AG 2026-07 accept novelty 8.0 of 10

    A higher-dimensional Kummer construction associates K3^[3]-type hyper-Kähler sixfolds to Kum^3-type sixfolds, with applications to motives, derived categories, and algebraic cycle conjectures.

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