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  Serre algebra, matrix factorization and categorical Torelli theorem for hypersurfaces

Lin, X., & Zhang, S. (in press). Serre algebra, matrix factorization and categorical Torelli theorem for hypersurfaces. Mathematische Annalen, Published Online - Print pending. doi:10.1007/s00208-024-02915-8.

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2310.09927.pdf (Preprint), 214KB
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 Creators:
Lin, Xun1, Author           
Zhang, Shizhuo1, Author           
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: 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.

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Language(s): eng - English
 Dates: 2024
 Publication Status: Accepted / In Press
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 Rev. Type: No review
 Identifiers: arXiv: 2310.09927
DOI: 10.1007/s00208-024-02915-8
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Title: Mathematische Annalen
Source Genre: Journal
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Publ. Info: Springer
Pages: - Volume / Issue: - Sequence Number: Published Online - Print pending Start / End Page: - Identifier: -