Families of artinian and low dimensional determinantal rings |
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Authors: | Jan O. Kleppe |
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Affiliation: | Faculty of Technology, Art and Design, Oslo and Akershus University College of Applied Sciences, P.O. Box 4, St. Olavs Plass, NO-0130 Oslo, Norway |
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Abstract: | Let be the scheme parameterizing graded quotients of with Hilbert function H (it is a subscheme of the Hilbert scheme of if we restrict to quotients of positive dimension, see definition below). A graded quotient of codimension c is called standard determinantal if the ideal I can be generated by the minors of a homogeneous matrix . Given integers and , we denote by the stratum of determinantal rings where are homogeneous of degrees .In this paper we extend previous results on the dimension and codimension of in to artinian determinantal rings, and we show that is generically smooth along under some assumptions. For zero and one dimensional determinantal schemes we generalize earlier results on these questions. As a consequence we get that the general element of a component W of the Hilbert scheme of is glicci provided W contains a standard determinantal scheme satisfying some conditions. We also show how certain ghost terms disappear under deformation while other ghost terms remain and are present in the minimal resolution of a general element of . |
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Keywords: | Primary 13C40 14C05 13D10 secondary 14M12 13E10 13D02 13D07 13A02 13H10 |
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