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

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

1998-11-20

arxiv.org/abs/math/9811120v1

Mathematics

Algebraic Geometry

17 pages, PlainTeX

Scientific paper

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 (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.

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