On a class of quasihomogeneous affine varieties

We give a classification of irreducible affine algebraic varieties which are quasihomogeneous with respect to a regular action by a connected linear group of automorphisms and are such that the isotropy subgroup of a point in general position contains a maximal unipotent subgroup of the group of transformations. We find criteria for the normality and factoriality of such varieties. We compute the divisor class group and give a complete description of the orbits in such varieties.