Projections of cones and the arithmetical rank of toric varieties

الأصل · EN

Let Iₘ and Iₙ be defining ideals of toric varieties such that Iₘ is a projection of Iₙ, i.e. Iₙ Iₘ. 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.