Families of stable sheaves: Wrong-way fibers and noncommutative deformations

Abstract

In this thesis we want to understand properties of families of stable sheaves.

First we give a quick introduction to the topic. Then we look at three specific topics regarding families of stable sheaves: a) stability of wrong-way fibers, b) wrong-way fibers and integral functors and c) noncommutative surfaces and deformations.

For each topic we collect known results and describe the state-of-the-art methods to study these properties. We end each section with open questions. Then we give a quick summary of our results answering some of the open questions.