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

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arxiv 2208.00073 v1 pith:NQDV5ETX submitted 2022-07-29 math.RT math.COmath.CT

Wen Chang , Yu Qiu , Xiaoting Zhang This is my paper · ORCID
classification math.RTmath.COmath.CT
keywords mathbfoperatornamestabilitycategorydynkingeometricmodelmodule
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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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  1. Contractibility and total semi-stability conditions of Euclidean quivers

    math.RT 2025-01 conditional novelty 6.0 of 10

    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.

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