2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60639We prove the invariance of plurigenera under smooth projective deformations in full generality. The proof is done by several estimates of singular hermitian metrics in terms of $L^{2}$-extension theorem of holomorphic sections.15pages, no figure introduction was expanded and misquoted Theorem 2.4 is correctedAlgebraic Geometry32J25text