Show simple item record

dc.contributor.authorKleppe, Jan Oddvar
dc.identifier.citationKleppe, J.O. (2017). Families of artinian and low dimensional determinantal rings. Journal of Pure and Applied Algebra doi:10.1016/j.jpaa.2017.05.001language
dc.description.abstractLet GradAlg(H) be the scheme parameterizing graded quotients of R = k[x_0,...,x_n] with Hilbert function H (it is a subscheme of the Hilbert scheme of P^n if we restrict to quotients of positive dimension, see definition below). A graded quotient A = R/I of codimension c is called standard determinantal if the ideal I can be generated by the t×t minors of a homogeneous t×(t+c−1) matrix (f_ij). Given integers a_0 ≤ a_1 ≤ ... ≤ a_{t+c−2} and b_1≤...≤b_t, we denote by W_s(b;a)⊂ GradAlg(H) the stratum of determinantal rings where f_ij ∈ R are homogeneous of degree a_j−b_i. In this paper we extend previous results on the dimension and codimension of W_s(b;a) in GradAlg(H) to artinian determinantal rings, and we show that GradAlg(H) is generically smooth along W_s(b;a) 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 P^n 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 GradAlg(H).language
dc.relation.ispartofseriesJournal of Pure and Applied Algebra;
dc.titleFamilies of artinian and low dimensional determinantal rings.language
dc.typeJournal articlelanguage
dc.typePeer reviewedlanguage
dc.source.journalJournal of Pure and Applied Algebra

Files in this item


This item appears in the following Collection(s)

Show simple item record
Except where otherwise noted, this item's license is described as