Algebraicity criteria for almost homogeneous complex spaces
Let \(G\) be a connected reductive complex Lie group acting on a normal irreducible complex space \(X\) with the property that there is a point \(x_0 \in X\) such that the orbit \(G\cdot x_0\) is open in \(X\). The author proves that: if the isotropy group \(G_{x_0}\) is connected and if there are points \(x_1,x_2, \dots,x_r\) such that the isotropy groups \(G_{x_1}, \dots, G_{x_r}\) are reductive and moreover for every \(x\in X\) the closure of the orbit \(G\cdot x\) contains at least one of the \(x_i\), then \(X\) is a complex algebraic \(G\)-variety. This result has an application for the algebraicity criterion for Moishezon spaces. For the proof the author uses the results of \textit{P. Heinzner} [Math. Ann. 289, 631-662 (1991; Zbl 0738.32010)].
scientific article; zbMATH DE number 1462963