Star configurations are set-theoretic complete intersections

Abstract

Let A⊂Pk-1 be a rank k arrangement of n hyperplanes, with the property that any k of the defining linear forms are linearly independent (i.e., $${\mathcal{A}}$$A is called k-generic). We show that for any j=0,…,k-2, the subspace arrangement with defining ideal generated by the (n − j)-fold products of the defining linear forms of A is a set-theoretic complete intersection, which is equivalent to saying that star configurations have this property.