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Stability Conditions and Algebraic Hearts for Acyclic Quivers (2510.08961v1)
Published 10 Oct 2025 in math.RT and math.AG
Abstract: We study stability conditions on the derived category of a finite connected acyclic quiver. We prove that, for any stability condition on the derived category, its heart can be obtained from an algebraic heart by a rotation of phases. Consequently, we establish the connectedness of the space of stability conditions. Furthermore, we prove that every stability condition $\sigma$ admits a full $\sigma$-exceptional collection.
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