Study On The Minimal Number Of Elements Describing An Algebraic Set

The problem about the minimal number of elements needed to describe an algebraic set is an outstanding and difficult problem in algebraic geometry.This paper is devoted to present studies on this problem set theoretically,and we mainly discuss several classic issues which still unsolved in characteristic 0 here.In particular,the thesis points out that the third method to show that all monomial space curves are set-theoretic complete intersections,thus simplifying the process to come to this conclusion.At the same time,we also extend the classic result that all the monomial space curves in p~3 which are arithmetically Cohen-Macaulay are set-theoretic complete intersections to some more general algebraic sets. In addition,this paper also carry on some other relevant discussion to complete intersection.