Journal of Lie Theory

no. 1
On the Geometry of Normal Horospherical G-Varieties of Complexity One
Journal of Lie Theory, Volume 26 (2016) no. 1, pp. 49-78
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.
DOI: 10.5802/jolt.880
Classification: 14L30, 14M27, 14M17
Keywords: 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},
     number = {1},
     doi = {10.5802/jolt.880},
     zbl = {1391.14091},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.880/}
}
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K. Langlois; R. Terpereau. On the Geometry of Normal Horospherical G-Varieties of Complexity One. Journal of Lie Theory, Volume 26 (2016) no. 1, pp. 49-78. doi: 10.5802/jolt.880

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