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We give a explicit description of gluing stability conditions on ruledsurfaces by introducing gluing perversity. Moreover, we describe adestabilizing wall of skyscraper sheaves on ruled surfaces by deformation ofstability conditions glued from $\widetilde{GL^{+}}(2,\mathbb{R})$-translatesof the standard stability condition on the base curve.

Explicit Description of A Certain Destabilizing Wall of Skyscraper Sheaves on Ruled Surfaces