# Conditions de stabilit\'e et g\'eom\'etrie birationnelle [d'apr\`es Bridgeland, Bayer-Macr\`i, ...]

## TL;DR

This paper surveys stability conditions in algebraic geometry, focusing on their application to the birational geometry of holomorphic symplectic varieties, with insights from Bridgeland and Bayer-Macrì.

## Contribution

It provides a comprehensive overview of stability conditions and explores their implications in the birational geometry of specific complex varieties.

## Key findings

- Stability conditions relate to the birational geometry of holomorphic symplectic varieties.
- Applications include understanding the structure of derived categories on surfaces.
- Connections to Bridgeland and Bayer-Macrì's work are highlighted.

## Abstract

We survey some aspects of stability conditions both in general and on the derived category of coherent sheaves on a surface, with applications to the birational geometry of certain holomorphic symplectic varieties.