[en] A new framework is found for the compactification of supersymmetric string theory. It is shown that the massless spectra of critical string vacua with central charge c=3D_crit can be derived from manifolds of complex dimension D_crit+2(Q-1),Q≥1, whose first Chern class is quantized in a particular way. This new class is more general than that of Calabi-Yau manifolds because it contains spaces corresponding to vacua with no Kaehler deformations, i.e., no antigenerations, thus providing mirrors of rigid Calabi-Yau manifolds. The constructions introduced here lead to new insights into the relation between Landau-Ginzburg vacua on the one hand and Calabi-Yau manifolds on the other