Hilbert scheme strata defined by bounding cohomology

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

2005-09-06

arxiv.org/abs/math/0509126v1

Mathematics

Commutative Algebra

21 pages. Short version of my Ph.D. thesis (math.AC/0509123)

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 paper is to show that some of these subspaces are connected. For this we exploit the edge ideals constructed by D. Mall. It turns out that these ideals are sequentially Cohen-Macaulay and that their initial ideals with respect to the reverse lexicographic term order are generic initial ideals.

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