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 $V \twoheadrightarrow \mathscr{L}$ considered in arXiv:1811.12525, 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 $\mathbb{P}(\mathscr{L})$-sections and the respective dual sections of a given HPD pair.