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...(X) 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...(X) ->(X) are of Fourier-Mukai type when..,.. ' belong to these classes of varieties, as predicted by a conjecture of Kuznetsov.
Derived categories of hearts on Kuznetsov components / C. Li, L. Pertusi, X. Zhao. - In: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6107. - 108:6(2023 Dec), pp. 2146-2174. [10.1112/jlms.12804]
Derived categories of hearts on Kuznetsov components
L. Pertusi
;
2023
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...(X) 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...(X) ->(X) are of Fourier-Mukai type when..,.. ' belong to these classes of varieties, as predicted by a conjecture of Kuznetsov.File | Dimensione | Formato | |
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