We prove the generic Torelli theorem for hypersurfaces in $\mathbb {P}^{n}$ of degree $d$ dividing $n+1$, for $d$ sufficiently large. Our proof involves the higher-order study of the variation of… Click to show full abstract
We prove the generic Torelli theorem for hypersurfaces in $\mathbb {P}^{n}$ of degree $d$ dividing $n+1$, for $d$ sufficiently large. Our proof involves the higher-order study of the variation of Hodge structure along particular one-parameter families of hypersurfaces that we call ‘Schiffer variations.’ We also analyze the case of degree $4$. Combined with Donagi's generic Torelli theorem and results of Cox and Green, this shows that the generic Torelli theorem for hypersurfaces holds with finitely many exceptions.
Keywords:
variations generic;
theorem hypersurfaces;
torelli theorem;
generic torelli;
schiffer variations
Journal Title: Compositio Mathematica
Year Published: 2022
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Journal Title: Compositio Mathematica
Year Published: 2022
Link to full text (if available)
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recommendations!