Families of Artinian and onedimensional algebras
Abstract
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 Hilbert function H. Let B > A be any graded surjection of quotients of R with Hilbert function H_B=(1,h_1,...,h_j,...) and H_A respectively. If dim A = 0 (resp. dim A = depth A = 1) and A is a "truncation" of B in the sense that H_A=(1,h_1,...,h_{j1},s,0,0,...) (resp. H_A=(1,h_1,...,h_{j1},s,s,s,...)) for some s < 1+h_j, then we show there is a close relationship between GradAlg^{H_A}(R) and GradAlg^{H_B}(R) concerning e.g. smoothness and dimension at the points (A) and (B) respectively, provided B is a complete intersection or provided the CastelnuovoMumford regularity of A is at least 3 (sometimes 2) larger than the regularity of B. In the complete intersection case we generalize this relationship to "nontruncated" Artinian algebras A which are compressed or close to being compressed. For more general Artinian algebras we describe the dual of the tangent and obstruction space of deformations in a manageable form which we make rather explicit for level algebras of CohenMacaulay type 2. This description and a linkage theorem for families allow us to prove a conjecture of Iarrobino on the existence of at least two irreducible components of GradAlg^H(R), H=(1,3,6,10,14,10,6,2), whose general elements are Artinian level algebras of type 2.
Collections
Date
2007Author
Kleppe, Jan Oddvar
Related items
Showing items related by title, author, creator and subject.

Unobstructedness and dimension of families of Gorenstein algebras
Kleppe, Jan Oddvar (Universitat de Barcelona, 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 ... 
The Dirac operator on compact quantum groups
Neshveyev, Sergey; Tuset, Lars (Walter de Gruyter, 20100120)For the qdeformation Gq, 0 < q < 1, of any simply connected simple compact Lie group G we construct an equivariant spectral triple which is an isospectral deformation of that defined by the Dirac operator D on G. Our ... 
Families of Determinantal Schemes
Kleppe, Jan Oddvar; MiroRoig, Rosa Maria (American Mathematical Society, 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) ...