Connectedness of Hilbert scheme strata defined by bounding cohomology

Details Connectedness of Hilbert scheme strata defined by bounding cohomology Connectedness of Hilbert scheme strata defined by bounding cohomology

2005-09-06

arxiv.org/abs/math/0509123v1

Mathematics

Commutative Algebra

67 pages, Ph.D. thesis

Scientific paper

Let Hilb^p be the Hilbert scheme parametrizing the closed subschemes of P^n with Hilbert polynomial p \in Q[t] over a field K of characteristic zero. By bounding below the cohomological Hilbert functions of the points of Hilb^p 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 ideals constructed by D. Mall. It turns out that these ideals are sequentially Cohen-Macaulay and that their initial ideals and their generic initial ideals coincide for any admissible term order.

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