Transfinite Stability Conditions on Derived Categories of Coherent Sheaves for Calabi-Yau Threefolds

Mathematical Applications of Science Fiction We construct a continuous family of Bridgeland stability conditions on the bounded derived category of coherent sheavesDb(Coh(X)) for a smooth projective Calabi-Yau threefold X. By utilizing a double-tilting procedure of the standard heartvia the generalized Bogomolov-Gieseker (BG) inequality, we establish the existence of stability conditions in the largevolume limit. We rigorously prove the support property for the constructed central charge Zα,β and demonstrate that theassociated heart Aα,β satisfies the Harder-Narasimhan property. Furthermore, we analyze the wall-crossing behavior ofstable objects under deformations of the Kähler class, providing a transfinite induction argument for the preservation ofstability across countably many walls of type II.