Browsing ODA Open Digital Archive by Author "Kleppe, Jan Oddvar"
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Comparison theorems for deformation functors via invariant theory
Christophersen, Jan Arthur; Kleppe, Jan Oddvar (Collectanea Mathematica;January 2019, Volume 70, Issue 1, Journal article; Peer reviewed, 20180906)We compare deformations of algebras to deformations of schemes in the setting of invariant theory. Our results generalize comparison theorems of Schlessinger and the second author for projective schemes. We consider ... 
Components of the Hilbert scheme of space curves on lowdegree smooth surfaces
Kleppe, Jan Oddvar; Ottem, John Christian (International Journal of Mathematics;26(2), Journal article; Peer reviewed, 20150227)We study maximal families W of the Hilbert scheme, H(d, g)sc, of smooth connected space curves whose general curve C lies on a smooth surface S of degree s. We give conditions on C under which W is a generically smooth ... 
Deformations of modules of maximal grade and the Hilbert scheme at determinantal schemes
Kleppe, Jan Oddvar (Journal of Algebra;407, Journal article; Peer reviewed, 20140404)Let R be a polynomial ring and M a finitely generated graded Rmodule of maximal grade (which means that the ideal I_t(\cA) generated by the maximal minors of a homogeneous presentation matrix, \cA, of M has maximal ... 
Families of artinian and low dimensional determinantal rings.
Kleppe, Jan Oddvar (Journal of Pure and Applied Algebra;, Journal article; Peer reviewed, 2017)Let 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 ... 
Families of Artinian and onedimensional algebras
Kleppe, Jan Oddvar (Journal of Algebra;311, Journal article; Peer reviewed, 2007)The purpose of this paper is to study families of Artinian or one dimensional quotients of a polynomial ring R with a special look to level algebras. Let GradAlg^H(R) be the scheme parametrizing graded quotients of R with ... 
Families of Determinantal Schemes
Kleppe, Jan Oddvar; MiroRoig, Rosa Maria (Proceedings of the American Mathematical Society;, Journal article; Peer reviewed, 20110316)Given integers a_0 <= a_1 <= ... <= a_{t+c2} and b_1 <= ... <= b_t, we denote by W(b;a) \subset Hilb^p(P^n) the locus of good determinantal schemes X in P^n of codimension c defined by the maximal minors of a t x (t+c1) ... 
Families of low dimensional determinantal schemes
Kleppe, Jan Oddvar (Journal of Pure and Applied Algebra;215 (7), Journal article; Peer reviewed, 20101109)A scheme X in P^n of codimension c is called standard determinantal if its homogeneous saturated ideal can be generated by the t x t minors of a homogeneous t x (t+c1) matrix (f_{ij}). Given integers a_0 <= a_1 <= ... <= ... 
The Hilbert Scheme of Buchsbaum space curves
Kleppe, Jan Oddvar (Annales de l'Institut Fourier;62, Journal article; Peer reviewed, 2012)We consider the Hilbert scheme H(d,g) of space curves C with homogeneous ideal I(C):=H_{*}^0(\sI_C) and Rao module M:=H_{*}^1(\sI_C). By taking suitable generizations (deformations to a more general curve C') of C, we ... 
Ideals generated by submaximal minors
Kleppe, Jan Oddvar; MiroRoig, Rosa Maria (Algebra & Number Theory;3 (4), Journal article; Peer reviewed, 2009)The goal of this paper is to study irreducible families W(b;a) of codimension 4, arithmetically Gorenstein schemes X of P^n defined by the submaximal minors of a t x t matrix A whose entries are homogeneous forms of degree ... 
Liaison invariants and the Hilbert scheme of codimension 2 subschemes in P^{n+2}
Kleppe, Jan Oddvar (Progress in Mathematics;Vol. 280, Chapter; Peer reviewed, 2010)In this paper we study the Hilbert scheme, Hilb(P), of equidimensional locally CohenMacaulay codimension 2 subschemes, with a special look to surfaces in P^4 and 3folds in P^5, and the Hilbert scheme stratification H_c ... 
Moduli Spaces of Reflexive Sheaves of Rank 2
Kleppe, Jan Oddvar (Canadian Journal of Mathematics;62 (5), Journal article; Peer reviewed, 2010)Let F be a coherent rank 2 sheaf on a scheme Y in P^n of dimension at least two. In this paper we study the relationship between the functor which deforms a pair (F,s), s in H^0(F), and the functor which deforms the ... 
On the normal sheaf of determinantal varieties
Kleppe, Jan Oddvar; MiroRoig, Rosa M. (Journal für die Reine und Angewandte Mathematik;, Journal article; Peer reviewed, 20140618)Let X be a standard determinantal scheme X of P^n of codimension c, i.e. a scheme defined by the maximal minors of a tx(t+c1)homogeneous polynomial matrix A. In this paper, we study the main features of its normal sheaf ... 
The Hilbert scheme of space curves sitting on a smooth surface containing a line
Kleppe, Jan Oddvar (Peer reviewed; Journal article, 20161014)We continue the study of maximal families W of the Hilbert scheme, H(d,g)_{sc}, of smooth connected space curves whose general curve C lies on a smooth degrees surface S containing a line. For s > 3, we extend the two ... 
Unobstructedness and dimension of families of codimension 3 ACM algebras
Kleppe, Jan Oddvar; MiroRoig, Rosa Maria (Contemporary Mathematics;448, Journal article; Peer reviewed, 2007)The goal of this paper is to study irreducible families of codimension 3, CohenMacaulay quotients A of a polynomial ring R=k[x_0,x_1,...,x_n]; mainly, we study families of graded CohenMacaulay quotients A of codimension ... 
Unobstructedness and dimension of families of Gorenstein algebras
Kleppe, Jan Oddvar (Collectanea Mathematica; 58(2), Journal article; Peer reviewed, 2007)The goal of this paper is to develop tools to study maximal families of Gorenstein quotients A of a polynomial ring R. We prove a very general Theorem on deformations of the homogeneous coordinate ring of a scheme Proj A ...