Star Configurations are Set-Theoretic Complete Intersections

الأصل · EN

Let Aᵏ⁻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., 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.