The moduli space of total semi-stability conditions on Euclidean quivers is described by partition data and contracts linearly to any non-concentrated stability condition.
Geometric model for module categories of Dynkin quivers via hearts of total stability conditions
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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.
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Contractibility and total semi-stability conditions of Euclidean quivers
The moduli space of total semi-stability conditions on Euclidean quivers is described by partition data and contracts linearly to any non-concentrated stability condition.