Tilting and torsion pairs

We define the torsion pairs and work out the details of Lemma 6.3 and Exercise 6.4 of Macrì-Schmidt's notes. We go on with Definition 6.6, work out the details of Exercise 6.7 and at least mention Exercise 6.8. State Theorem 6.10 and 6.13. Some words about the classical(!) Bogomolov inequality and its relevance in classical geometry. We sketch the proof of Theorem 6.14.

Finally, discuss stability conditions on K3: we introduce all we need to state Theorem 6.1. In particular, we introduce the notion of spherical object and mention Lemma 6.2.