HILBERT SCHEME OF A PAIR OF CODIMENSION TWO LINEAR SUBSPACES

Abstract. We study the component Hn of the Hilbert scheme whose general point parameterizes a pair of codimension two linear subspaces in Pn for n ≥ 3. We show that Hn is smooth and isomorphic to the blow-up of the symmetric square of G(n−2, n) along the diagonal. Further Hn intersects only one other component in the full Hilbert scheme, transversely. We determine the stable base locus decomposition of its effective cone and give modular interpretations of the corresponding models, hence conclude that Hn is a Mori dream space. 1