2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/120739T. Bridgeland defined the notion of a stability manifold for a triangulated category, motivated by Douglas's work on Π-stability for D-branes. We show that the stability manifold of the bounded derived category of the coherent sheaves on P^1 is C^2. This is the first complete picture of a stability manifold for a non-Calabi-Yau manifold.Lots of minor collections made and explanations addedAlgebraic GeometryCategory Theorytext