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arXiv · 2509.11405

Stability conditions on irreducible projective curves

Ziqi Liu
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Abstract

This note revisits stability conditions on the bounded derived categories of coherent sheaves on irreducible projective curves. In particular, all stability conditions on smooth curves are classified and a connected component of the stability manifold containing all the geometric stability conditions is identified for singular curves. On smooth curves of positive genus, the set of all non-locally-finite stability conditions gives a partial boundary of any known compactification of the stability manifold. To provide a reasonable full boundary, a notion of regular weak stability condition is proposed based on the definition of Collins-Lo-Shi-Yau and is classified for smooth curves of positive genus. On non-rational singular curves, any locally-finite numerical stability condition is shown to be geometric.

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Ziqi Liu. 2025-09-14. Stability conditions on irreducible projective curves. https://arxiv.org/abs/2509.11405

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