2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/169329In this note, we shall show that the Chow-stability and the Hilbert-stability in GIT asymptotically coincide.I slightly changed the title of the paper. Moreover, a proof using an equivariant version of Serre's Conjecture is given. This new version appeared in Osaka J. Math. 45 (2008)Differential GeometryAlgebraic Geometry32Q15; 14L24text