The stability space of the derived category of holomorphic triples and further investigations

Abstract

In this thesis we give a complete description of the Bridgeland stability space for the bounded derived category of holomorphic triples over a smooth projective curve of genus one as a connected, four dimensional complex manifold.

We will then prove a number of helpful facts that characterise the bounded derived category of holomorphic triples and will subsequently generalise some of the results on the stability space of the bounded derived category of holomorphic triples to that of holomorphic chains.