An introduction to the birational geometry of moduli spaces of stable objects

Diletta Martinelli (Edinburgh)

Abstract

I will explain how hyperkaehler varieties arise as one of the building blocks in the birational classification of algebraic varieties. Then I will describe how recent advances have made possible to apply the machinery of wall-crossing and stability conditions on derived categories, originally developed by Tom Bridgeland to formalize concepts arising from string theory, to study the birational geometry of hyperkaehler varieties of K3-type. I will keep the talk to an introductory/motivational level, more than focusing on the technicalities of the subjects.