2022/03/25 by Chunyi Li, Laura Pertusi, Li, Chunyi +3 · 1 citation
Mathematics · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Algebraic Geometry and Number Theory
paper · pdf · doi:10.48550/arxiv.2203.13864
We prove a general criterion which guarantees that an admissible subcategory 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 has a strongly unique dg enhancement, applying the recent results of Canonaco, Neeman and Stellari. We apply this criterion to the Kuznetsov component \mathopKu(X) when X is a cubic fourfold, a Gushel--Mukai 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 \mathopKu(X) \xrightarrow∼ \mathopKu(X') are of Fourier--Mukai type when X, X' belong to these classes of varieties, as predicted by a conjecture of Kuznetsov.