
Journal of Lie Theory 26 (2016), No. 1, 049078 Copyright Heldermann Verlag 2016 On the Geometry of Normal Horospherical GVarieties of Complexity One Kevin Langlois Instituto de Ciencias Matematicas, Campus Cantoblanco, UAM, Universidad Autónoma de Madrid, Madrid 28049, Spain langlois.kevin18@gmail.com Ronan Terpereau Fachbereich Physik, Mathematik und Informatik, JohannesGutenbergUniversität, 55099 Mainz, Germany rterpere@unimainz.de Let G be a connected simplyconnected reductive algebraic group. In this article, we consider the normal algebraic varieties equipped with a horospherical Gaction such that the quotient of a Gstable open subset is a curve. Let X be such a Gvariety. 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 logterminal, respectively. Keywords: LunaVust theory, colored polyhedral divisors, normal Gvarieties. MSC: 14L30, 14M27, 14M17 [ Fulltextpdf (547 KB)] for subscribers only. 