Singular complex-symmetric torus embeddings
Let T be an algebraic torus. A compact torus embedding is by definition a (normal) compactification X of T such that the natural action of T on itself extends to an algebraic action on X. We call X complex-symmetric if each point \(x\in X\) is isolated fixed point of a T-equivariant holomorphic involution which is called a holomorphic symmetry. Here we prove that each singular complex-symmetric torus embedding can be obtained as the quotient of a smooth complex-symmetric torus embedding by a finite subgroup of the torus. Since smooth complex-symmetric torus embeddings are classified in a former paper [Ann. Inst. Fourier 39, No.2, 373-416 (1989; Zbl 0649.32021)] the structure of these varieties is now very well understood. However, by giving a counterexample one shows that such a quotient is not necessarily complex-symmetric. This result also completes the classification of normal complex-symmetric spaces with a reductive automorphism group which was begun in the paper quoted above.
classification of almost-homogeneous spaces
classification of almost- homogeneous varieties
scientific article; zbMATH DE number 4142447