Stability conditions on derived categories

Abstract

<p>My thesis is divided into two parts. In the first part I consider stability conditions on the derived category of complex manifolds without any nontrivial subvarieties. In particular, I construct and classify stability conditions in the case of generic K3 surfaces, generic tori and general deformations of Hilbert schemes of K3 surfaces. <br /> The second part is devoted to the analysis of quotient categories. The main theorem of the second part states that the quotient category of the derived category of a surface modulo complexes supported in codimension two has homological dimension one. I apply this to describe the quotient category obtained by modding out Mumford-stable objects of degree zero.</p>