Abstract:
In this paper almost transitive actions of linear algebraic groups G are studied on complete normal manifolds X defined over the field of complex numbers. Such actions are completely described in cases when the complement in X of an open orbit is disconnected or contains an isolated point. As a preliminary, all homogeneous spaces of G having two Freudenthal ends are found.
Bibliography: 16 titles.
This publication is cited in the following 12 articles:
Bruno Laurent, “Almost Homogeneous Varieties of Albanese Codimension One”, International Mathematics Research Notices, 2022:10 (2022), 7304
Ahmadi R., Gilligan B., “Classification of Kahler Homogeneous Manifolds of Non-Compact Dimension Two”, Ann. Scuola Norm. Super. Pisa-Cl. Sci., 17:4 (2017), 1231–1254
Ahmadi S.R., Gilligan B., “Complexifying Lie Group Actions on Homogeneous Manifolds of Non-Compact Dimension Two”, Can. Math. Bul.-Bul. Can. Math., 57:4 (2014), 673–682
Ivan Arzhantsev, M. G. Zaidenberg, K. G. Kuyumzhiyan, “Flag varieties, toric varieties, and suspensions: Three instances of infinite transitivity”, Sb. Math., 203:7 (2012), 923–949
Kishimoto T., Prokhorov Yu., Zaidenberg M., “Group Actions on Affine Cones”, Affine Algebraic Geometry: the Russell Festschrift, CRM Proceedings & Lecture Notes, 54, eds. Daigle D., Ganong R., Koras M., Amer Mathematical Soc, 2011, 123–163
Giuliana Gigante, “Hyperbolicity outside a compact set and homogeneous spaces”, Annali di Matematica, 176:1 (1999), 73
Alan Huckleberry, Aspects of Mathematics, E 26, Contributions to Complex Analysis and Analytic Geometry / Analyse Complexe et Géométrie Analytique, 1994, 189
V. L. Popov, E. B. Vinberg, Encyclopaedia of Mathematical Sciences, 55, Algebraic Geometry IV, 1994, 123
D. N. Akhiezer, “On the concept of the rank of a spherical homogeneous space”, Russian Math. Surveys, 43:5 (1988), 205–206
F. Lescure, “Elargissement du groupe d'automorphismes pour des vari�t�s quasi-homogenes”, Math. Ann., 261:4 (1982), 455
Bruce Gilligan, “Ends of complex homogeneous manifolds having non-constant holomorphic functions”, Arch. Math, 37:1 (1981), 544
A. T. Huckleberry, E. Oeljeklaus, Manifolds and Lie Groups, 1981, 159
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