My own case comes from dynamic system on compact complex manifolds. To be precise, let $M$ be a compact complex 3-dimentional manifold, $W^c$ a holomorphic foliation of M with 1-dimentional uniformly compact leaves(i.e. the leaves are compact Riemann surfaces and the holonomy groups are finite.)

It can be deduced from above that the leaves with non-trivial holonomy are finite. Then $M/W^c$ is a obifold with complex dimension 2 with finite singular points $x$ whose neighborhood $U_x$ is homeomorphic to $\mathbb C^2/\Gamma_x$ where $\Gamma_x=\Gamma_x^s \times \Gamma_x^u$ and $\Gamma_x^s<O(2),\Gamma_x^y<O(2)$. Both groups $\Gamma_x^s$ and $\Gamma_x^u$ have the same order.

My question is that whether $M$ is good(i.e. it arises as the quotient of a simply connected manifold by a proper rigid action of a discrete group Γ) Is it purely a topological problem, or the complex structure can help us to eliminate the singulartity ?