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.
Ziqi Liu (Sun,) studied this question.