2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/99925Let C be the contact structure naturally induced on the lens space L(p,q) by the standard contact structure on the three--sphere. We obtain a complete classification of the symplectic fillings of (L(p,q),C) up to orientation-preserving diffeomorphisms. In view of our results, we formulate a conjecture on the diffeomorphism types of the smoothings of complex two-dimensional cyclic quotient singularities.45 pages, 9 figures; a few typos corrected; accepted for publication in Trans. Amer. Math. SocSymplectic GeometryGeometric Topology57R17; 53D35text