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arXiv · 1108.2099

The space of stability conditions for quivers with two vertices

Takahisa Shiina
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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 $P_n$ 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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Takahisa Shiina. 2011-08-10. The space of stability conditions for quivers with two vertices. https://arxiv.org/abs/1108.2099

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