Algebraic Geometry Student's Seminar : Boundedness of Numerically Trivial Line Bundles

In this talk, we will prove a boundedness theorem for numerically trivial line bundles. In the course of the proof I will introduce tools that have a wide array of applications such as vanishing theorems, Castelnuovo-Mumford regularity and the Quot scheme. The main purpose of the talk is not the theorem itself but rather to give an example of how these powerful tools are used.