\(T^ n\)-actions on holomorphically separable complex manifolds
We study holomorphically separable n-dimensional complex manifolds M equipped with an effective \(T^ n\)-action. Our results relate the possibility of realizing M concretely as a Reinhardt domain or as an open subset of a toroidal embedding to various function-theoretic properties, such as the existence of a suitable envelope of holomorphy for M. Our method involves the study of a certain semigroup which is related to the Fourier expansion of holomorphic functions on M as well as to the isotropy subgroups for the group action. Our methods give rise in particular to new examples of (three- dimensional) holomorphically separable complex manifolds M for which \({\mathcal O}(M)\) is not a Stein algebra. (The first such example is due to Grauert.)
scientific article; zbMATH DE number 4061630
scientific article