Geometric model for module categories of Dynkin quivers via hearts of total stability conditions

Abstract

We derive a geometric model for the module category $\operatorname{mod} \mathbf{k} Q$ of a Dynkin quiver $Q$ via the heart of a total stability condition on the bounded derived category of $\operatorname{mod} \mathbf{k} Q$. As an application, we prove Reineke's conjecture that there is a stability function on $\operatorname{mod} \mathbf{k} Q$ making any indecomposables stable.