The manifold of stability conditions

Here we want to study the structure of the set of Bridgeland stability conditions. We first explain what a generalised metric is and we introduce the topology on the set of stability conditions Stab(X). We introduce the action of GL(2, R) and state Theorem 5.14 of Macrì-Schmidt's notes. Explain why this is equivalent to the "more useful" Proposition 5.15. Next discuss space of stability conditions for curves as in Example 5.16.

Define the walls (Definition 5.25) and discuss the "openness of stability" as in Prop. 5.26 (No proof asked!). Discuss as this can be effectively checked with Cor 5.29. (Time permitting, it would be good to see proof of Lemma 5.28!).