Z_N×Z_M orbifolds and discrete torsion

We extend previous work on Z_N-orbifolds to the general Z_N×Z_M abelian case for the (2, 2) and (0, 2) models. We classify the corresponding (2, 2) compactifications and show that a number of models obtined by tensoring minimal N = 2 superconformal theories can be constructed as Z_N×Z_M-orbifolds. Furthermore, Z_N×Z_M-orbifolds allow the addition of discrete torsion which leads to new (2, 2) compactifications not considered previously. Some of the latter have negative Euler characteristic and Betti numbers equal to those of some complete intersection Calabi-Yau (CICY) manifolds. This suggests the existence of a previously overlooked connection between CICY models and orbifolds.