The Gauss map of a smooth doubly{curved surface characterizes the range of variation of the surface normal as an area on the unit sphere. An algorithm to approximate the Gauss map boundary to any desired accuracy is presented, in the context of a tensor{product polynomial surface patch, r(u;v) for (u; v) 2 0; 1 ] 0; 1 ]. Boundary segments of the Gauss map correspond to variations of the normal ...

Given a singular projective variety in some space, we characterize the smooth curves contracted by Gauss map terms of normal bundles. As consequence, show that if is not linear, then line always has local obstruction for embedded deformation and each component Hilbert scheme where lies non-reduced everywhere.