On the set-theoretic complete intersection problem for monomial curves in An and Pn

Abstract

In this paper we deal with the problem of the expression of monomial curves in the affine or projective n-dimensional space as set-theoretic complete intersections. We develop two techniques for finding monomial curves which are set-theoretic complete intersections. Using these two techniques we are able to generalize all previous known results and give infinitely many examples of monomial curves which are set-theoretic complete intersections in an affine or projective n-dimensional space, for any n.