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Mathematisch-Naturwissenschaftliche Fakultät - Jahrgang 2008

 

Titel

Stability conditions on derived categories

Autor

Sven Meinhardt

Publikationsform

Dissertation

Abstract

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.
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.

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© Universitäts- und Landesbibliothek Bonn | Veröffentlicht: 2008