Infinitesimal categorical Torelli theorems for Fano threefolds

Let X be a smooth Fano variety and Ku(X) its Kuznetsov component. A Torelli theorem for states that is uniquely determined by certain polarized abelian associated to it. An infinitesimal the differential of period map injective. categorical variant morphism η:H1(X,TX)→HH2(Ku(X)) In present article, we use machinery Hochschild (co)homology relate aforementioned three Torelli-type theorems varieties via commutative diagram. As an application, prove class prime threefolds. We then prove, infinitesimally, restatement Debarre–Iliev–Manivel conjecture regarding general fibre ordinary Gushel–Mukai