Why should a birational geometer care about Bridgeland stability conditions?

TL;DR

This survey explains how Bridgeland stability conditions are relevant to birational geometry, illustrating their application through an example, and makes the topic accessible without prior knowledge of derived categories.

Contribution

It provides an accessible overview of Bridgeland stability conditions and their applications in birational geometry, bridging a gap for newcomers.

Findings

Bridgeland stability conditions can be applied to problems in birational geometry.

The survey demonstrates a specific example of this application.

It removes the need for prior knowledge of derived categories.

Abstract

In this survey we borrow from Coskun and Huizenga an example of application of Bridgeland stability conditions to birational geometry and we rephrase it without assuming any previous knowledge about derived categories.