On compact orbits in singular Kähler spaces
Given a solvable complex Lie group \(G\) which acts holomorphically on a compact Kähler manifold \(X\), there exists a subtorus \(T\) of the Albanese variety \(Alb (X)\) such that every closed orbit is a torus isogenous to \(T\). The preceding result as pointed out by the author was generalized to singular Kähler spaces in the paper. Recall that a compact complex space \(X\) is of class \({\mathcal C}\) if \(X\) is bimeromorphic to a compact Kähler manifold. The theorem proved here asserts that if \(X\) is of class \({\mathcal C}\) and \(G\) a solvable complex Lie group acting on \(X\), then any two compact \(G\)-orbits are tori isogenous to each other and furthermore isogenous to the \(G\)-orbits in the Albanese of any equivariant desingularization of \(X\).
scientific article; zbMATH DE number 1089885