Geodesic
The structure of the canonical module and the Gorenstein property for some quasihomogeneous varieties
Sbornik. Mathematics, Tome 65 (1990) no. 1, pp. 81-95 Cet article a éte moissonné depuis la source Math-Net.Ru

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The canonical module for quasihomogeneous affine varieties with the property that the stabilizer of a point from the open orbit contains a maximal unipotent subgroup is described in terms of the structure of the semigroup of dominant weights defining the variety. A criterion for such a variety to be Gorenstein is also given. Bibliography: 18 titles. 
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D. I. Panyushev. The structure of the canonical module and the Gorenstein property for some quasihomogeneous varieties. Sbornik. Mathematics, Tome 65 (1990) no. 1, pp. 81-95. http://geodesic.mathdoc.fr/item/SM_1990_65_1_a3/

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