Schiffer variations of hypersurfaces and the generic Torelli theorem

Abstract: The generic Torelli theorem for hypersurfaces of degree d and dimension n-1 was proved by Donagi in the 90's. It works under the assumption that d is at least 7 and d does not divide n+1, which in particular excludes the Calabi-Yau case in all dimensions. We prove that the generic Torelli theorem for hypersurfaces holds with finitely many exceptions. A key tool is the notion of Schiffer variation of a hypersurface and how to characterize them by looking at the variation of Hodge structure along them.

algebraic geometry

Audience: researchers in the topic

Western Algebraic Geometry ONline

Series comments: Description: Conference in algebraic geometry

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