THE CANONICAL MODULE OF A QUASI-HOMOGENEOUS NORMAL AFFINE SL(2)-VARIETY

For the varieties mentioned in the title a description is given for the canonical divisor, the Picard group, and the divisor class group. In particular, it follows from this that the singular 3-dimensional quasihomogeneous SL2-varieties are not Gorenstein. The canonical module is described. All descriptions are given in terms of discrete parameters: the height and the degree of a quasihomogeneous affine SL2-variety.