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 factorization category as a derivedequivalent
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 homo-logical projective duals for (relative) d-Veronese embeddings, recovering the sheaf of
Clifford algebras obtained by Kuznetsov in the case when d = 2.