Actions of Linear Algebraic Groups on Projective Manifolds and Minimal Model Program

الأصل · EN

Let 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 (rG +1), where rG is the minimum codimension of the maximal parabolic subgroup of G (for instance rSL(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.