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Mathematics, Algebraic Geometry, Mathematical Physics, Mathematics
Abstract:
Let X be a smooth Fano variety. We attach a bi-graded associative algebra AS=⨁i,j∈ZHom(Id,SiKu(X)[j]) to the Kuznetsov component Ku(X) whenever it is defined. Then we construct a natural sub-algebra of AS when X is a Fano hypersurface and establish its relation with Jacobian ring J(X). As an application, we prove a categorical Torelli theorem for Fano hypersurface X⊂Pn(n≥2) of degree d if gcd(n+1,d)=1. In addition, we give a new proof of the [Pir22,Theorem1.2] using a similar idea.
