2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/221238In the case of two-dimensional cyclic quotient singularities, we classify all one-parameter toric deformations in terms of certain Minkowski decompositions. In particular, we describe to which components each such deformation maps, show how to induce each deformation from a versal family, give explicit equations for each deformation, describe the singularities in the general fibers, and construct the corresponding partial simultaneous resolutions.18 pages, 3 figures; v2 minor revisions; v3 strengthened main theoremAlgebraic Geometry14B07; 14M25text