Study On The Complete Intersections Of Monomial Curves

It is well known that a algebraic variety in an n-space can be written as the intersection of n hypersurfaces.Natural to ask whether this number is minimal.Actually,complete intersection signifies the minimum equation which is to describe the algebraic variety.That is,if a curve in n-space is set-theoritic complete intersection,then the curve is the intersection of n-1 hypersurfaces.The problem of whether all monomial curves are set-theoretic complete intersections is still open.The mail result of this thesis is:Theorem A:Let C be a monomial curve in P_K~n,where K is a field of characteristic zero. Then C is a binomial set theoretic complete intersection if and only if C is a ideal-theoretic complete intersection.Besides,in this thesis I give a new proof of the theorem 3.1 of A.Thoma in[6].