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arXiv · 2208.00073

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

Wen Chang·Yu Qiu·Xiaoting Zhang
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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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Wen Chang, Yu Qiu, Xiaoting Zhang. 2022-07-29. Geometric model for module categories of Dynkin quivers via hearts of total stability conditions. https://arxiv.org/abs/2208.00073

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