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TY - JOUR AU - Ahiezer, Dmitry PY - 1983 DA - 1983/02/01 TI - Equivariant completions of homogenous algebraic varieties by homogenous divisors JO - Annals of Global Analysis and Geometry SP - 49 EP - 78 VL - 1 IS - 1 AB - Complete smooth complex algebraic varieties with an almost transitive action of a linear algebraic group are studied. They are classified in the case, when the complement of the open orbit is a homogeneous hypersurface. If the group and the isotropy subgroup at a generic point are both reductive, then there exists a natural one-to-one correspondence between these two-orbit varieties and compact riemannian symmetric spaces of rank one. SN - 1572-9060 UR - https://doi.org/10.1007/BF02329739 DO - 10.1007/BF02329739 ID - Ahiezer1983 ER -