Geodesic
On the Geometry of Normal Horospherical G-Varieties of Complexity One
Journal of Lie theory, Tome 26 (2016) no. 1, pp. 49-78
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Let G be a connected simply-connected reductive algebraic group. In this article, we consider the normal algebraic varieties equipped with a horospherical G-action such that the quotient of a G-stable open subset is a curve. Let X be such a G-variety. Using the combinatorial description of Timashev, we describe the class group of X by generators and relations and we give a representative of the canonical class. Moreover, we obtain a smoothness criterion for X and a criterion to determine whether the singularities of X are rational or log-terminal, respectively.
Classification : 14L30, 14M27, 14M17
Mots-clés : Luna-Vust theory, colored polyhedral divisors, normal G-varieties 
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     author = {K. Langlois and R. Terpereau},
     title = {On the {Geometry} of {Normal} {Horospherical} {G-Varieties} of {Complexity} {One}},
     journal = {Journal of Lie theory},
     pages = {49--78},
     year = {2016},
     volume = {26},
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     url = {http://geodesic.mathdoc.fr/item/JLT_2016_26_1_JLT_2016_26_1_a2/}
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K. Langlois; R. Terpereau. On the Geometry of Normal Horospherical G-Varieties of Complexity One. Journal of Lie theory, Tome 26 (2016) no. 1, pp. 49-78. http://geodesic.mathdoc.fr/item/JLT_2016_26_1_JLT_2016_26_1_a2/