| Abstrakt: |
We prove a general criterion that guarantees that an admissible subcategory K$\mathcal {K}$ 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 K$\mathcal {K}$ has a strongly unique dg enhancement, applying the recent results of Canonaco, Neeman, and Stellari. We apply this criterion to the Kuznetsov component Ku(X)$\mathop {\mathcal {K}u}\nolimits (X)$ when X$X$ 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 Ku(X)→∼Ku(X′)$\mathop {\mathcal {K}u}\nolimits (X) \xrightarrow {\sim } \mathop {\mathcal {K}u}\nolimits (X^{\prime })$ are of Fourier–Mukai type when X$X$, X′$X^{\prime }$ belong to these classes of varieties, as predicted by a conjecture of Kuznetsov. [ABSTRACT FROM AUTHOR] |
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