The space of stability conditions for quivers with two vertices
arXiv:1108.2099
Abstract
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 with two vertices and 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.
18 pages. Rewrite the introduction, including main theorem. Added references. Corrected typos. Rewrite some proofs