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Hilbert scheme strata defined by bounding cohomology


Fumasoli, S (2007). Hilbert scheme strata defined by bounding cohomology. Journal of Algebra, 315(2):566-587.

Abstract

Let Hilbp be the Hilbert scheme parametrizing the closed subschemes of with Hilbert polynomial over a field K of characteristic zero. By bounding below the cohomological Hilbert functions of the points of Hilbp 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.

Abstract

Let Hilbp be the Hilbert scheme parametrizing the closed subschemes of with Hilbert polynomial over a field K of characteristic zero. By bounding below the cohomological Hilbert functions of the points of Hilbp 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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2007
Deposited On:10 Dec 2009 16:26
Last Modified:18 Feb 2018 12:51
Publisher:Elsevier
ISSN:0021-8693
Additional Information:Short version of Ph.D. thesis
OA Status:Hybrid
Free access at:Related URL. An embargo period may apply.
Publisher DOI:https://doi.org/10.1016/j.jalgebra.2007.04.016
Related URLs:http://arxiv.org/abs/math/0509126

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