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We show how to recover a general hypersurface in $\mathbb{P}^n$ ofsufficiently large degree $d$ dividing $n+1$, from its finite order variationof Hodge structure. We also analyze the two other series of cases not coveredby Donagi's generic Torelli theorem. Combined with Donagi's theorem, this showsthat the generic Torelli theorem for hypersurfaces holds with finitely manyexceptions.

Schiffer variations and the generic Torelli theorem for hypersurfaces