A complex associated to a family of ideals and applications to subspace arrangements

Abstract

We reprove and generalize a result of Derksen describing the Hilbert polynomial of the vanishing ideal of a transversal subspace arrangement in projective space. When the subspaces have all codimension 2, we describe explicitly the local cohomology modules of the corresponding defining ideal. This is achieved via a complex naturally associated to the subspace arrangement, whose basic properties are also investigated.