Lectures on Bridgeland Stability

TL;DR

This paper provides an introductory overview of Bridgeland stability conditions on smooth complex projective varieties, focusing on surfaces, covering definitions, moduli spaces, and stability variation, based on lecture series.

Contribution

It offers a comprehensive introduction to Bridgeland stability conditions, including foundational concepts and their applications to moduli spaces, tailored for researchers and students.

Findings

Clarifies the definition of Bridgeland stability conditions

Explains the structure of moduli spaces of stable objects

Discusses the variation of stability conditions

Abstract

In these lecture notes we give an introduction to Bridgeland stability conditions on smooth complex projective varieties with a particular focus on the case of surfaces. This includes basic definitions of stability conditions on derived categories, basics on moduli spaces of stable objects and variation of stability. These notes originated from lecture series by the first author at the summer school "Recent advances in algebraic and arithmetic geometry", Siena, Italy, August 24-28, 2015 and at the school "Moduli of Curves", CIMAT, Guanajuato, Mexico, February 22 - March 4, 2016.