Derived category of projectivization and generalized linear duality

Abstract

In this note, we generalize the linear duality between vector subbundles (or equivalently quotient bundles) of dual vector bundles to coherent quotients V L considered in [JL18c], in the framework of Kuznetsov's homological projective duality (HPD). As an application, we obtain a generalized version of the fundamental theorem of HPD for the P(L )-sections and the respective dual sections of a given HPD pair.

Derived category of projectivizations and flops

“…then this can be viewed as the dual situation of the above structure theorem. The duality between projectivization of above G and the blowing up formulae can be formulated precisely in the framework of homological projective duality (HPD), see [39].…”