论文标题
Kuznetsov组件上的心脏类别
Derived categories of hearts on Kuznetsov components
论文作者
论文摘要
我们证明了一个通用标准，该标准可以保证Abelian类别的派生类别的可允许的子类别$ \ MATHCAL {K} $等同于有界T结构的核心核心类别。结果，我们表明$ \ Mathcal {K} $具有强烈的DG增强功能，并应用了Canonaco，Neeman和Stellari的最新结果。我们将此标准应用于Kuznetsov组件$ \ MATHOP {\ MATHCAL {k} u}（x）$时，$ x $是立方四倍，gushel- mukai-mukai品种或Quartic Double solid。特别是，我们得到这些kuznetsov组件具有强烈独特的DG增强功能，并且形式的确切等价是$ \ Mathop {\ MathCal {\ Mathcal {k} u}（x）\ xrightArrow {\ sim} {\ sim} \ m arterop {\ mathcal {\ mathcal {k} u}（k} u}（k} u}（x'）品种，如Kuznetsov的猜想所预测。
We prove a general criterion which guarantees that an admissible subcategory $\mathcal{K}$ 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 $\mathcal{K}$ has a strongly unique dg enhancement, applying the recent results of Canonaco, Neeman and Stellari. We apply this criterion to the Kuznetsov component $\mathop{\mathcal{K}u}(X)$ 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 $\mathop{\mathcal{K}u}(X) \xrightarrow{\sim} \mathop{\mathcal{K}u}(X')$ are of Fourier--Mukai type when $X$, $X'$ belong to these classes of varieties, as predicted by a conjecture of Kuznetsov.
