Which points are in this point set depends on the field . If then the set is empty, there are no absolute points (and no absolute hyperplanes). On the other hand, if the set of absolute points form a nondegenerate quadric (a conic in two-dimensional space). If is a finite field of odd characteristic the absolute points also form a quadric, but if the characteristic is even the absolute points form a hyperplane (this is an example of a pseudo polarity).