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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 dimensionalrepresentations 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 werestrict it to the complement of a line arrangement. When the number of arrowsis greater than two we need to remove uncountably many lines to obtain acovering map.

The space of stability conditions for quivers with two vertices