Ordinary cohomology groups of $(\mathbb{C}^3\times T^2)/\mathbb{Z}_k$ that I need for my string theory research Hmm, I don't think so. for k=4, aren't the "two points" of type $C^4/Z_2$ identified by the $Z_4$ action? Similarly for $k=6$. Anyway, the configurations of the fixed points follow the length of the legs of Dynkin diagrams of $D_4$, $E_{6,7,8}$, and constrained by the fact that 1/2+1/2+1/2+1/2=1/3+1/3+1/3=1/4+1/4+1/2=1/6+1/3+1/2=1 ...