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  1. ; ; (, International Mathematics Research Notices)
    Abstract We construct singular quartic double fivefolds whose Kuznetsov component admits a crepant categorical resolution of singularities by a twisted Calabi–Yau threefold. We also construct rational specializations of these fivefolds where such a resolution exists without a twist. This confirms an instance of a higher-dimensional version of Kuznetsov’s rationality conjecture and of a noncommutative version of Reid’s fantasy on the connectedness of the moduli of Calabi–Yau threefolds. 
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    Free, publicly-accessible full text available May 1, 2026
  2. ; ; (, ANNALI DELL'UNIVERSITA' DI FERRARA)
    Abstract Using the algebraic criterion proved by Bandiera, Manetti and Meazzini, we show the formality conjecture for universally gluable objects with linearly reductive automorphism groups in the bounded derived category of a K3 surface. As an application, we prove the formality conjecture for polystable objects in the Kuznetsov components of Gushel–Mukai threefolds and quartic double solids. 
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  3. ; ; (, Journal of the London Mathematical Society)
    Abstract We prove a general criterion that guarantees that an admissible subcategory of the derived category of an abelian category is equivalent to the bounded derived category of the heart of a bounded t‐structure. As a consequence, we show that has a strongly unique dg enhancement, applying the recent results of Canonaco, Neeman, and Stellari. We apply this criterion to the Kuznetsov component when is a cubic fourfold, a GM variety, or a quartic double solid. In particular, we obtain that these Kuznetsov components have strongly unique dg enhancement and that exact equivalences of the form are of Fourier–Mukai type when , belong to these classes of varieties, as predicted by a conjecture of Kuznetsov. 
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  4. ; ; (, Algebraic Geometry)
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  5. ; ; (, Advances in Mathematics)
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  6. ; ; (, Translations American Mathematical Society)
    Accepted Manuscript Full Text Available
  7. ; ; (, Mathematische Zeitschrift)
    Abstract We prove that two Enriques surfaces defined over an algebraically closed field of characteristic different from 2 are isomorphic if their Kuznetsov components are equivalent. This improves and completes our previous result joint with Nuer where the same statement is proved for generic Enriques surfaces. 
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  8. ; ; (, Geometry & Topology)
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  9. ; ; ; (, Mathematische Annalen)
    Abstract We prove that two general Enriques surfaces defined over an algebraically closed field of characteristic different from 2 are isomorphic if their Kuznetsov components are equivalent. We apply the same techniques to give a new simple proof of a conjecture by Ingalls and Kuznetsov relating the derived categories of the blow-up of general Artin–Mumford quartic double solids and of the associated Enriques surfaces. 
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