2014/09/19 by Ballard, Matthew, Deliu, Dragos, Favero, David +2
#Algebraic Geometry (math.AG) #Category Theory (math.CT) #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1409.5568
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.