On simplicial toric varieties which are set-theoretic complete intersections
The paper is devoted to the determination of the minimum number of equations needed to define set-theoretically an algebraic variety \(V\) (the arithmetical rank of \(I=I(V)\), denoted by ara\((I))\). If \(h(I)=\text{ara}(I)\) (where \(h(I)\) denotes as usual the height of \(I)\) the ideal \(I\) is called a set-theoretic complete intersection, and when ara\((I)\leq h(I)+1\) it is called almost set-theoretically complete intersection. The authors prove that every simplicial toric affine or projective variety with full parametrization is an almost set-theoretically complete intersection; the same is true for every simplicial toric (affine or projective) variety of codimension two. If the characteristic is positive then every simplicial toric affine or projective variety with full parametrization is actually a set-theoretically complete intersection.
scientific article; zbMATH DE number 1448617