S ep 2 00 5 Connectedness of Hilbert Scheme Strata Defined by Bounding Cohomology

Let HilbpK be the Hilbert scheme parametrizing the closed subschemes of Pn K with Hilbert polynomial p ∈ Q[t] over a field K of characteristic zero. By bounding below the cohomological Hilbert functions of the points of HilbpK we define locally closed subspaces of the Hilbert scheme. The aim of this thesis is to show that some of these subspaces are connected. For this we exploit the binomial ideals constructed by D. Mall in [Mal00]. It turns out that these binomial ideals are sequentially Cohen-Macaulay and that their initial ideals and their generic initial ideals coincide for any admissible term order.