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 investigate necessary conditions for Gorenstein projective varieties to admit
semiorthogonal decompositions introduced by Kawamata, with main emphasis on threefolds …

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 …

This thesis consists of three parts and is a collection of papers written by the author of this
text during his postgraduate studies, together with an Appendix chapter. The first chapter is …

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 …