On the one dimensional polynomial and regular images of R-n

Abstract

In this work we present a full geometric characterization of the 1-dimensional polynomial and regular images of R-n. In addition, given a polynomial image S of R-n, we compute the smallest positive integer p := p(S) such that S is a polynomial image of R-p. Analogously, given a regular image S' of R-n, we determine the smallest positive integer r := r(S') such that S' is a regular image of R-r.