Geodesic
Contractions of affine spherical varieties
Sbornik. Mathematics, Tome 190 (1999) no. 7, pp. 937-954 
I. V. Arzhantsev. Contractions of affine spherical varieties. Sbornik. Mathematics, Tome 190 (1999) no. 7, pp. 937-954. http://geodesic.mathdoc.fr/item/SM_1999_190_7_a0/
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     title = {Contractions of affine spherical varieties},
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     url = {http://geodesic.mathdoc.fr/item/SM_1999_190_7_a0/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The language of filtrations and contractions is used to describe the class of $G$-varieties obtainable as the total spaces of the construction of contraction applied to affine spherical varieties, which is well-known in invariant theory. These varieties are local models for arbitrary affine $G$-varieties of complexity 1 with a one-dimensional categorical quotient. As examples, reductive algebraic semigroups and three-dimensional $\operatorname{SL}_2$-varieties are considered.

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