The space of stability conditions for quivers with two vertices

Details The space of stability conditions for quivers with two vertices The space of stability conditions for quivers with two vertices

2011-08-10

arxiv.org/abs/1108.2099v1

Mathematics

K-Theory and Homology

17 pages

Scientific paper

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.

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