We prove a generalization of Orlov's projectivization formula for the derived category D coh
b (P (E)), where E does not need to be a vector bundle; Instead, E is a coherent sheaf which …

We introduce the notion of a categorical join, which can be thought of as a categorification of
the classical join of two projective varieties. This notion is in the spirit of homological …

Kuznetsov's homological projective duality (HPD) theory [K4] is one of the most active and
powerful recent developments in the homological study of algebraic geometry. The …

This paper develops two theories, the geometric theory of derived Grassmannians (and flag
schemes) and the algebraic theory of derived Schur (and Weyl) functors, and establishes …

In this paper, we construct and classify a new family of flips, called generalized
Grassmannian flips, by generalizing the construction of standard flips for $\mathbb {P} …

In this note, we generalize the linear duality between vector subbundles (or equivalently
quotient bundles) of dual vector bundles to coherent quotients $ V\twoheadrightarrow …

We investigate the DK conjecture on derived categories of coherent sheaves stated by
Bondal-Orlov and Kawamata: there should be a derived embedding for any flip and in …