2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77741Let X be a smooth projective variety of dimension n on which a simple Lie group G acts regularly and non trivially. Then X is not minimal in the sense of the Minimal Model Program. In the paper we work out a classification of X via the Minimal Model Program under the assumption that the dimension of X is small with the respect to the dimension of G. More precisely we classify all such X with n smaller or equal to (r_G +1), where r_G is the minimum codimension of the maximal parabolic subgroup of G (for instance r_{SL(m)}= m-1). We consider also the case when G = SL(3) and X is a smooth 4-fold on which G acts with an open orbit.17 pages, PlainTeXAlgebraic Geometry14L30, 14E30 (Primary) 14L35 14J40 (Secondary)text