2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/141855Let (X,L) be a polarised manifold. We show that K-stability and asymptotic Chow stability of the blowup of X along a 0-dimensional cycle are closely related to Chow stability of the cycle itself, for polarizations making the exceptional divisors small. This can be used to give (almost) a converse to a result of Arezzo and Pacard, and to give new examples of Kähler classes with no constant scalar curvature representatives.19 pages. Many improvements. To appear in J. Algebraic GeometryAlgebraic GeometryDifferential Geometry53C55text