Full exceptional collections and stability conditions for Dynkin quivers

Abstract

For a stability condition $\sigma$ on a triangulated category, Dimitrov-Katzarkov introduced the notion of a $\sigma$-exceptional collection. In this paper, we study full $\sigma$-exceptional collections in the derived category of an acyclic quiver. In particular, we prove that any stability condition $\sigma$ on the derived category of a Dynkin quiver admits a full $\sigma$-exceptional collection.