Introduction to stability conditions

Understand

These are notes of a course given at the 'school on moduli spaces' at the Newton Institute in January 2011.

• The abstract theory of stability conditions (due to Bridgeland and Douglas) on abelian and triangulated categories is developed via tilting and t-structures.
• Special emphasis is put on the bounded derived category of coherent sheaves on smooth projective varieties (in particular for curves and K3 surfaces).
• The lectures were targeted at an audience with little prior knowledge of triangulated categories and stability conditions but with an interest in vector bundles on curves.