Biregular models of log Del Pezzo surfaces with rigid singularities

We construct biregular models of families of log Del Pezzo surfaces with rigid cyclic quotient singularities such that a general member in each family is wellformed and quasismooth. Each biregular model consists of infinite series of such families of surfaces; parameterized by the natural numbers . Each family in these biregular models is represented by either a codimension 3 Pfaffian format modelled on the Plücker embedding of Gr(2, 5) or a codimension 4 format modelled on the Segre embedding of ² ײ. In particular, we show the existence of two biregular models in codimension 4 which are biparameterized, giving rise to an infinite series of models of families of log Del Pezzo surfaces. We identify those biregular models of surfaces which do not admit a -Gorenstein deformation to a toric variety.