copy of the thesis has been supplied on the condition that anyone who consults it is understood to recognise that its copyright rests with its author and that no quotation from the thesis and no information derived from it may be published without the prior written consent of the author. This thesis may be made available for consultation within the… (More)
We explain a method for calculating the cohomology of line bundles on a toric variety in terms of the cohomology of certain constructible sheaves on the polytope. We show its effective use by means of some examples.
We study the derived categories of smooth projective toric surfaces and show that the group of autoequivalences is generated by the standard equivalences and spherical twists obtained from −2-curves. We also prove a close link between spherical objects and certain pairs of exceptional objects. In this article, we study the derived categories of smooth,… (More)
We ask when a finite set of t-structures in a triangulated category can be 'averaged' into one t-structure or, equivalently, when the extension closure of a finite set of aisles is again an aisle. There is a straightforward, positive answer for a finite set of compactly generated t-structures in a big triangulated category. For piecewise tame hereditary… (More)