Projections of cones and the arithmetical rank of toric varieties

Let IM and IN be defining ideals of toric varieties such that IM is a projection of IN, i.e. INsubset of or equal toIM. We give necessary and sufficient conditions for the equality IM=rad(IN+(f1,…,fs)), where f1,…,fs belong to IM. Also, a method for finding toric varieties which are set-theoretic complete intersection is given. Finally, we apply our method in the computation of the arithmetical rank of certain toric varieties and provide the defining equations of the above toric varieties.