We have analyzed the influence of the stellar populations , from which SN progenitors come from , on the observational outcome , including the metal free Pop . III . We use our models to study the evolution of the progenitor , the subsequent explosion and the light curves . For Type Ia , the variation of the main sequence mass of the progenitor of the exploding WD , produces an offset in the maximum-decline relation of 0.2 mag . This effect is critical for the use of high redshift Type Ia SNe as cosmological standard candles . In contrast , the metallicity does not change the above relation ( at maximum , \Delta M _ { V } \leq 0.06 mag ) . For Type II , we find a dependence of the light curve properties with both , main sequence mass and metallicity of the progenitor , and we identify a rather homogeneous subclass , Extreme II-P , that may be used as a quasi-standard candle . Note that , although not as good as Type Ia for distance determinations , Type II are expected to occur since the first stars were formed .