On the derived categories of degree d hypersurface fibrations

We provide descriptions of the derived categories of degree d hypersurface fibrations which generalize a result of Kuznetsov for quadric fibrations and give a relative version of a well-known theorem of Orlov. Using a local generator and Morita theory, we re-interpret the resulting matrix factorizat...

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Bibliographic Details
Published in:Mathematische annalen 2018-06, Vol.371 (1-2), p.337-370
Main Authors: Ballard, Matthew, Deliu, Dragos, Favero, David, Isik, M. Umut, Katzarkov, Ludmil
Format: Article
Language:English
Subjects:
Algebra
Homology
Mathematics
Mathematics and Statistics
Perturbation methods
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Summary:We provide descriptions of the derived categories of degree d hypersurface fibrations which generalize a result of Kuznetsov for quadric fibrations and give a relative version of a well-known theorem of Orlov. Using a local generator and Morita theory, we re-interpret the resulting matrix factorization category as a derived-equivalent sheaf of dg-algebras on the base. Then, applying homological perturbation methods, we obtain a sheaf of A ∞ -algebras which gives a new description of homological projective duals for (relative) d -Veronese embeddings, recovering the sheaf of Clifford algebras obtained by Kuznetsov in the case when d = 2 .
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-017-1613-4