The space of stability conditions for $A_3$-quiver

The author studied in \cite{shi} the covering map property of the local homeomorphism associating to the space of stability conditions over the $n$-Kronecker quiver. In this paper, we discuss the covering map property for stability conditions over the Dynkin quiver of type $A_3$. The local homeomorphism from a connected component of stability conditions over $A_3$ to 3-dimensional complex vector space becomes a covering map when we restrict it to the complement of six codimension one subspaces.