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TitleHilbert scheme strata defined by bounding cohomology
Author(s) Stefan Fumasoli
TypeArticle in Journal
AbstractLet Hilb p be the Hilbert scheme parametrizing the closed subschemes of P K n with Hilbert polynomial p ∈ 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 in [D. Mall, Connectedness of Hilbert function strata and other connectedness results, J. Pure Appl. Algebra 150 (2000) 175–205]. 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.
KeywordsHilbert scheme, Local cohomology, Mall ideals, Sequentially Cohen-Macaulayness
URL http://www.sciencedirect.com/science/article/pii/S0021869307002566
JournalJournal of Algebra
Pages566 - 587
Translation No
Refereed No