Arend Bayer : Stability and applications to birational and hyperkaehler geometry - lecture 2

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Abstract: This lecture series will be an introduction to stability conditions on derived categories, wall-crossing, and its applications to birational geometry of moduli spaces of sheaves. I will assume a passing familiarity with derived categories.
- Introduction to stability conditions. I will start with a gentle review of aspects of derived categories. Then an informal introduction to Bridgeland's notion of stability conditions on derived categories. I will then proceed to explain the concept of wall-crossing, both in theory, and in examples.
- Wall-crossing and birational geometry. Every moduli space of Bridgeland-stable objects comes equipped with a canonically defined nef line bundle. This systematically explains the connection between wall-crossing and birational geometry of moduli spaces. I will explain and illustrate the underlying construction.
- Applications : Moduli spaces of sheaves on K3K3 surfaces. I will explain how one can use the theory explained in the previous talk in order to systematically study the birational geometry of moduli spaces of sheaves, focussing on K3 surfaces.
Recording during the thematic meeting: "Algebraic geometry and complex geometry" the November 25, 2015 at the Centre International de Rencontres MathÃ©matiques (Marseille, France)
Filmmaker: Guillaume Hennenfent

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