The space of stability conditions for quivers with two vertices

The purpose of this article is to study the space of stability conditions $\stab(P_n)$ on the bounded derived category $\D^b(P_n)$ of finite dimensional representations of a quiver $P_n$ with two vertices and $n$ parallel arrows. There is a local homeomorphism $\z:\stab(P_n)\rightarrow\C^2$. We show that, when the number of arrows is one or two, the map is a covering map if we restrict it to the complement of a line arrangement. When the number of arrows is greater than two we need to remove uncountably many lines to obtain a covering map.

💡 Research Summary

The paper investigates the space of Bridgeland stability conditions on the bounded derived category of finite‑dimensional representations of the quiver (P_n), which consists of two vertices joined by (n) parallel arrows. The authors focus on the central charge map \