2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/137105The automorphism group of the Galois covering induced by a pluri-canonical generic covering of a projective space is investigated. It is shown that by means of such coverings one obtains, in dimensions one and two, serieses of specific actions of the symmetric groups $S_d$ on curves and surfaces not deformable to an action of $S_d$ which is not the full automorphism group. As an application, new DIF $\ne$ DEF examples for $G$-varieties in complex and real geometry are given.34 pagesAlgebraic Geometry14J50; 14H37; 14P99; 14J10text