论文标题
Fano三倍的无穷小型Torelli定理
Infinitesimal categorical Torelli theorems for Fano threefolds
论文作者
论文摘要
令$ x $为平滑的fano品种，$ \ nathcal {k} u（x）$ kuznetsov组件。 Torelli定理用于$ \ Mathcal {k} u（x）$说，它是由附在上面的两极分化的Abelian品种确定的。 $ x $的无穷小torelli定理说，该期间图的差异是注入性的。 $ x $的无限torelli定理的一个分类变体说，形态$ h^1（x，t_x）\xrightArrowηhh^2（\ Mathcal {k} u（x））$是indmentive。在本文中，我们使用Hochschild（CO）同源性的机械将三个Torelli-Type定理联系起来，以通过交换图来提供平滑的Fano品种。作为应用程序，我们首先证明了一类Prime Fano三倍的无限分类Torelli定理。然后，我们证明了DeBarre-Iliev-Manivel猜想的重述。
Let $X$ be a smooth Fano variety and $\mathcal{K}u(X)$ the Kuznetsov component. Torelli theorems for $\mathcal{K}u(X)$ says that it is uniquely determined by a polarized abelian variety attached to it. An infinitesimal Torelli theorem for $X$ says that the differential of the period map is injective. A categorical variant of infinitesimal Torelli theorem for $X$ says that the morphism $H^1(X,T_X)\xrightarrowη HH^2(\mathcal{K}u(X))$ is injective. In the present article, we use the machinery of Hochschild (co)homology to relate the three Torelli-type theorems for smooth Fano varieties via a commutative diagram. As an application, we first prove infinitesimal categorical Torelli theorem for a class of prime Fano threefolds. Then we prove a restatement of the Debarre-Iliev-Manivel conjecture infinitesimally.
