2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/123054We prove some general statements on stability conditions of Calabi-Yau surfaces and discuss the stability manifold of the cotangent bundle of P^1. Our primary interest is in spherical objects.15 pages, revised in responce to referee's comments, to appear in IMRNAlgebraic GeometryK-Theory and Homologytext