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.