Dual String Pairs With N=1 And N=2 Supersymmetry In Four Dimensions

Based on a simple adiabatic argument and by considering the heterotic string counterpart of certain symmetries of Type II superstrings such as $(-1)^{F_L}$ and orientation reversal, we construct orbifold candidates for dual pairs of heterotic and Type II string theories with $N=2$ and $N=1$ supersymmetry. We also analyze from a similar point of view the ${\rm K3}$ fibrations that enter in recently proposed $N=2$ candidates and use this structure together with certain orientation-reversing symmetries to construct $N=1$ dual pairs. These pairs involve generalizations of Type I vacua which can be equivalent to $E_8\times E_8$ heterotic strings, while standard Type I vacua are related to $SO(32)$.