A categorical Torelli theorem for hypersurfaces

Let be a smooth Fano hypersurface of dimension and degree . The derived category of coherent sheaves on contains an interesting subcategory called the Kuznetsov component . We show that this subcategory, together with a certain autoequivalence called the rotation functor, determines uniquely if or if and . This generalizes a result by Huybrechts and Rennemo, who proved the same statement under the additional assumption that divides .