Projections of cones and the arithmetical rank of toric varieties

Let I-M and I-N be defining ideals of toric varieties such that I-M is a projection of I-N, i.e. I-N subset of I-M We give necessary and sufficient conditions for the equality I-M = rad(I-N + (f(1),..., f(s))), where f(1),..., f(s) belong to I-M. 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. (c) 2004 Elsevier B.V. All rights reserved.